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Unit 6 Test Review - Conic Sections Name_____ ©` V2a0j1i8y HKIuMtxar OSoodfFtFwraYrIeW lLfLPCy.B o FAwlSlL JrKibghhUtEsh vr[ezsVeJrVvhemdv. -1-Identify the ... If the graphs of a system of equations are two conic sections, the system may have zero, one, two, three, or four solutions. Some of the possible situations are shown below. no solutions one solution two solutions three solutions four solutions 456 Chapter 8 Conic Sections Use substitution to solve the system. First rewrite 4y x 3 as x 4y 3. Conic sections are a subsection of the bigger topic of analytic geometry or coordinate geometry. Just to refresh your memory, a right-regular cone is formed by revolving a right triangle around one of it's sides so that it "sweeps out" the shape of a cone. Let us briefly discuss the different conic sections formed when the plane cuts the nappes (excluding the vertex). Conic Section Circle. If β=90 o, the conic section formed is a circle as shown below. Conic Section Ellipse. If α<β<90 o, the conic section so formed is an ellipse as shown in the figure below. Conic Section Parabola Unit 6 Test Review - Conic Sections Name_____ ©` V2a0j1i8y HKIuMtxar OSoodfFtFwraYrIeW lLfLPCy.B o FAwlSlL JrKibghhUtEsh vr[ezsVeJrVvhemdv. -1-Identify the ...

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Conic Sections Circles, Parabolas, Ellipses & Hyperbolas The formulas for the conic sections are derived by using the distance formula, which was derived from the Pythagorean Theorem. If you know the distance formula and how each of the conic sections is defined, then deriving their formulas becomes simple.

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Unit 6 Test Review - Conic Sections Name_____ ©` V2a0j1i8y HKIuMtxar OSoodfFtFwraYrIeW lLfLPCy.B o FAwlSlL JrKibghhUtEsh vr[ezsVeJrVvhemdv. -1-Identify the ...

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21) The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 400ft apart and 100ft tall. If the supporting cable that runs from tower to tower is only The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. In this unit we study the conic sections. These are the curves obtained when a cone is cut by a plane. We find the equations of one of these curves, the parabola, by using an alternative description in terms of points whose distances from a fixed Math Formulas: Conic Sections The Parabola Formulas The standard formula of a parabola 1. y2 = 2px Parametric equations of the parabola: 2. x= 2pt2 y= 2pt Tangent line in a point D(x 0;y 0) of a parabola y2 = 2pxis : 3. y 0 y= p(x+ x 0) Tangent line with a given slope m: 4. y= mx+ p 2m Tangent lines from a given point Take a xed point P(x 0;y 0 ... The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.

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wps.prenhall.com Precalculus Notes: Unit 8 – Conic Sections Page 2 of 18 Precalculus – Graphical, Numerical, Algebraic: Pearson Chapter 6 Parabola: a locus of points in a plane equidistant from a fixed point (focus) and a fixed line (directrix) p = distance between focus to directrix and vertex Classify each conic section, write its equation in standard form, and sketch its graph. For parabolas, identify the vertex and focus. For circles, identify the center and radius. For ellipses and hyperbolas identify the center, vertices, and foci. 17) −2 y2 + x − 4y + 1 = 0 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 De nition 2. A conic section is the set of all points in a plane with the same eccentricity with respect to a particular focus and directrix. This leads to the following classi cations: Ellipses Conic sections with 0 e<1. Circles are the special case of e= 0. Parabolas Conic sections with e= 1. Hyperbolas Conic sections with e>1.

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The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.

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The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. Dec 12, 2019 · Download NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections शंकु परिच्छेद in PDF form. Students can do directly 12th class after doing 10th though NIOS Admission 2019-2020. Classifying conic sections Circles Parabola Ellipse Hyperbola Ax2+Cy2+Dx+Ey+F=0 A=C are not 0 AC>0 AC<0. hyperbol a parabo la ellipse . Title:

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Jun 12, 2019 · NCERT Solutions Class 11 Maths Chapter 11 Conic Sections – Here are all the NCERT solutions for Class 11 Maths Chapter 11. This solution contains questions, answers, images, explanations of the complete chapter 11 titled Of Conic Sections taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook … Conic section, also called conic, in geometry, any curve produced by the intersection of a plane and a right circular cone.Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola. Classifying conic sections Circles Parabola Ellipse Hyperbola Ax2+Cy2+Dx+Ey+F=0 A=C are not 0 AC>0 AC<0. hyperbol a parabo la ellipse . Title: Describe the conic section formed by the intersection of a double right cone and a plane. Determine the vertex form of a quadratic given the standard form Recognize how parameter changes affect the sketch of a conic section. Identify symmetries of conic sections Identify the conic section from an equation

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If the graphs of a system of equations are two conic sections, the system may have zero, one, two, three, or four solutions. Some of the possible situations are shown below. no solutions one solution two solutions three solutions four solutions 456 Chapter 8 Conic Sections Use substitution to solve the system. First rewrite 4y x 3 as x 4y 3. Conic Sections You might have come across such shapes when you cut a boiled egg vertically. The slice thus obtained represents an ellipse. Let us define the ellipse mathematically as follows: “An ellipse is the locus of a point which moves in a plane such that its distance Conic Sections Circles, Parabolas, Ellipses & Hyperbolas The formulas for the conic sections are derived by using the distance formula, which was derived from the Pythagorean Theorem. If you know the distance formula and how each of the conic sections is defined, then deriving their formulas becomes simple. Conic Sections and Standard Forms of Equations A conic section is the intersection of a plane and a double right circular cone . By changing the angle and location of the intersection, we can produce different types of conics. There are four basic types: circles , ellipses , hyperbolas and parabolas . None of the intersections will pass through ... ©Y Q2[0W1J6I ^KWuFt[aF oSSoJfdttwMaerget lLKLbC[.Q L xAUl`lc prMi[gdhDt[sM Zr`eesdeFr^vsezdF.v X ]MNaodEer hwXiftMh_ WIxnkfWimnTiRtieZ OAml`g_ewbArMaI c2T.

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Conic section, also called conic, in geometry, any curve produced by the intersection of a plane and a right circular cone.Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola. Dennis G. Zill and Jacqueline M. Dewar Precalculus with Calculus Previews FOURTH EDITION Chapter 6: Conic Sections 2007 and Bartlett Publishers

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Conic sections are graceful curves that can be defined in several ways and constructed by a wide variety of means. Most importantly, when a plane intersects a cone, the outline of a conic section results. This book will attempt the observation and manipulation of conic sections via their many definitions. Conic Sections Each conic section (or simply conic) can be described as the intersection of a plane and a double-napped cone. Notice in Figure 10.1 that for the four basic conics, the intersecting plane does not pass through the vertex of the cone. When the plane passes through the vertex, the resulting figure is a degenerate conic, as shown in ... Let us briefly discuss the different conic sections formed when the plane cuts the nappes (excluding the vertex). Conic Section Circle. If β=90 o, the conic section formed is a circle as shown below. Conic Section Ellipse. If α<β<90 o, the conic section so formed is an ellipse as shown in the figure below. Conic Section Parabola SECTION 11.5 • Conic Sections 5 A circle is a conic section formed by the intersection of a cone and a plane parallel to the base of the cone. A circle can be defined as all points in the plane that are a fixed distance from a

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The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.

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Conic sections are graceful curves that can be defined in several ways and constructed by a wide variety of means. Most importantly, when a plane intersects a cone, the outline of a conic section results. This book will attempt the observation and manipulation of conic sections via their many definitions. CONIC SECTIONS 239 In the following sections, we shall obtain the equations of each of these conic sections in standard form by defining them based on geometric properties. Fig 11. 8 Fig 11. 9 1. 10 11.3 Circle Definition 1 A circle is the set of all points in a plane that are equidistant from a fixed point in the plane. Describe the conic section formed by the intersection of a double right cone and a plane. Determine the vertex form of a quadratic given the standard form Recognize how parameter changes affect the sketch of a conic section. Identify symmetries of conic sections Identify the conic section from an equation Algebra Introduction to Conic Sections The intersection of a cone and a plane is called a conic section. There are four types of curves that result from these intersections that are of particular interest: Parabola Circle Ellipse Hyperbola

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Conic section, also called conic, in geometry, any curve produced by the intersection of a plane and a right circular cone.Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola. Jan 24, 2013 · CONIC SECTION In mathematics, a conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. Jun 12, 2019 · NCERT Solutions Class 11 Maths Chapter 11 Conic Sections – Here are all the NCERT solutions for Class 11 Maths Chapter 11. This solution contains questions, answers, images, explanations of the complete chapter 11 titled Of Conic Sections taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook … conic sections conics. GOAL 1 10.6 Graphing and Classifying Conics 623 Write and graph an equation of a parabola with its vertex at (h,k) and an equation of a circle, ellipse, or hyperbola with its center at (h, k). Classify a conic using its equation, as applied in Example 8. In the following equations the point (To model real-life situations ...

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Language has become an essential factor in students' performance in solving word problems, especially in the topic that requires multiple representations of terms such as conic sections. Conic Section is a curve formed by the intersection of a plane with the cone. The four sections of a cone are circle,ellipse,parabola and hyperbola. There is standard form for all the conic sections. A summary of Introduction to Conics in 's Conic Sections. Learn exactly what happened in this chapter, scene, or section of Conic Sections and what it means. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. C; The equation is of the form + + F = 0 , where = l, C = 5, E = 8, and F = —8. Since A and C have the same sign and A C, the graph is an ellipse. C; The equation is of the form + + F = 0 , where = l, C = 5, E = 8, and F = —8. Since A and C have the same sign and A C, the graph is an ellipse.

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Conic Sections Practice Test 1. Give the coordinates of the circle's center and it radius. ... Identify the conic by writing the equation in standard form.

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Jun 12, 2019 · NCERT Solutions Class 11 Maths Chapter 11 Conic Sections – Here are all the NCERT solutions for Class 11 Maths Chapter 11. This solution contains questions, answers, images, explanations of the complete chapter 11 titled Of Conic Sections taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook … In this unit we study the conic sections. These are the curves obtained when a cone is cut by a plane. We find the equations of one of these curves, the parabola, by using an alternative description in terms of points whose distances from a fixed Let us briefly discuss the different conic sections formed when the plane cuts the nappes (excluding the vertex). Conic Section Circle. If β=90 o, the conic section formed is a circle as shown below. Conic Section Ellipse. If α<β<90 o, the conic section so formed is an ellipse as shown in the figure below. Conic Section Parabola of a plane with a right circular cone. The three basic conic sections are the parabola, the ellipse, and the hyperbola (Figure 8.2a). Some atypical conics, known as , are shown in Figure 8.2b. Because it is atypical and lacks some of the features usually associated with an ellipse, degenerate conic sections conic section conic Axis Generator ...

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Conic Sections Practice Test 1. Give the coordinates of the circle's center and it radius. ... Identify the conic by writing the equation in standard form. ©Y Q2[0W1J6I ^KWuFt[aF oSSoJfdttwMaerget lLKLbC[.Q L xAUl`lc prMi[gdhDt[sM Zr`eesdeFr^vsezdF.v X ]MNaodEer hwXiftMh_ WIxnkfWimnTiRtieZ OAml`g_ewbArMaI c2T.

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De nition 2. A conic section is the set of all points in a plane with the same eccentricity with respect to a particular focus and directrix. This leads to the following classi cations: Ellipses Conic sections with 0 e<1. Circles are the special case of e= 0. Parabolas Conic sections with e= 1. Hyperbolas Conic sections with e>1. Dennis G. Zill and Jacqueline M. Dewar Precalculus with Calculus Previews FOURTH EDITION Chapter 6: Conic Sections 2007 and Bartlett Publishers Conic sections mc-TY-conics-2009-1 In this unit we study the conic sections. These are the curves obtained when a cone is cut by a plane. We ﬁnd the equations of one of these curves, the parabola, by using an alternative Conic Sections You might have come across such shapes when you cut a boiled egg vertically. The slice thus obtained represents an ellipse. Let us define the ellipse mathematically as follows: “An ellipse is the locus of a point which moves in a plane such that its distance

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Unit 6 Test Review - Conic Sections Name_____ ©` V2a0j1i8y HKIuMtxar OSoodfFtFwraYrIeW lLfLPCy.B o FAwlSlL JrKibghhUtEsh vr[ezsVeJrVvhemdv. -1-Identify the ...

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1 CHAPTER 2 CONIC SECTIONS 2.1 Introduction A particle moving under the influence of an inverse square force moves in an orbit that is a conic section; that is to say an ellipse, a parabola or a hyperbola. Jan 24, 2013 · CONIC SECTION In mathematics, a conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. ©Y Q2[0W1J6I ^KWuFt[aF oSSoJfdttwMaerget lLKLbC[.Q L xAUl`lc prMi[gdhDt[sM Zr`eesdeFr^vsezdF.v X ]MNaodEer hwXiftMh_ WIxnkfWimnTiRtieZ OAml`g_ewbArMaI c2T. Defining Conic Sections. A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic sections are the hyperbola, the parabola, and the ellipse. The circle is type of ellipse, and is sometimes considered to be a fourth type of conic section.

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Jun 12, 2019 · NCERT Solutions Class 11 Maths Chapter 11 Conic Sections – Here are all the NCERT solutions for Class 11 Maths Chapter 11. This solution contains questions, answers, images, explanations of the complete chapter 11 titled Of Conic Sections taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook … CONIC SECTIONS 239 In the following sections, we shall obtain the equations of each of these conic sections in standard form by defining them based on geometric properties. Fig 11. 8 Fig 11. 9 1. 10 11.3 Circle Definition 1 A circle is the set of all points in a plane that are equidistant from a fixed point in the plane. Conic sections are a subsection of the bigger topic of analytic geometry or coordinate geometry. Just to refresh your memory, a right-regular cone is formed by revolving a right triangle around one of it's sides so that it "sweeps out" the shape of a cone. Classify each conic section, write its equation in standard form, and sketch its graph. For parabolas, identify the vertex and focus. For circles, identify the center and radius. For ellipses and hyperbolas identify the center, vertices, and foci. 17) −2 y2 + x − 4y + 1 = 0 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 Jun 12, 2019 · NCERT Solutions Class 11 Maths Chapter 11 Conic Sections – Here are all the NCERT solutions for Class 11 Maths Chapter 11. This solution contains questions, answers, images, explanations of the complete chapter 11 titled Of Conic Sections taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook …

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Introduction to Conic Sections Conic sections were discovered during the classical Greek period, which lasted from 600 to 300 B.C. By the beginning of the Alexandrian period, enough was known of conics for A pollonius (262–190 B.C.) to produce an eight-volume work on the subject. Free PDF download of NCERT Solutions for Class 11 Maths Chapter 11 - Conic Sections solved by Expert Teachers as per NCERT (CBSE) Book guidelines. All Conic Sections Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks.

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Math Formulas: Conic Sections The Parabola Formulas The standard formula of a parabola 1. y2 = 2px Parametric equations of the parabola: 2. x= 2pt2 y= 2pt Tangent line in a point D(x 0;y 0) of a parabola y2 = 2pxis : 3. y 0 y= p(x+ x 0) Tangent line with a given slope m: 4. y= mx+ p 2m Tangent lines from a given point Take a xed point P(x 0;y 0 ... About This Quiz & Worksheet. Gauge how much you know about conic sections by completing this short multiple-choice quiz, which requires you to know how to find the radius of a circle and the ... Conic Sections You might have come across such shapes when you cut a boiled egg vertically. The slice thus obtained represents an ellipse. Let us define the ellipse mathematically as follows: “An ellipse is the locus of a point which moves in a plane such that its distance Introduction to Conic Sections Conic sections were discovered during the classical Greek period, which lasted from 600 to 300 B.C. By the beginning of the Alexandrian period, enough was known of conics for A pollonius (262–190 B.C.) to produce an eight-volume work on the subject.

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The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. This section covers: Tables of Conics Circles Applications of Circles Parabolas Applications of Parabolas Ellipses Applications of Ellipses Hyperbolas Applications of Hyperbolas Identifying the Conic More Practice Conics (circles, ellipses, parabolas, and hyperbolas) involves a set of curves that are formed by intersecting a plane and a double-napped right cone (probably too much information ... 21) The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 400ft apart and 100ft tall. If the supporting cable that runs from tower to tower is only Introduction to Conic Sections Conic sections were discovered during the classical Greek period, which lasted from 600 to 300 B.C. By the beginning of the Alexandrian period, enough was known of conics for A pollonius (262–190 B.C.) to produce an eight-volume work on the subject.

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©Y Q2[0W1J6I ^KWuFt[aF oSSoJfdttwMaerget lLKLbC[.Q L xAUl`lc prMi[gdhDt[sM Zr`eesdeFr^vsezdF.v X ]MNaodEer hwXiftMh_ WIxnkfWimnTiRtieZ OAml`g_ewbArMaI c2T. 21) The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 400ft apart and 100ft tall. If the supporting cable that runs from tower to tower is only About This Quiz & Worksheet. Gauge how much you know about conic sections by completing this short multiple-choice quiz, which requires you to know how to find the radius of a circle and the ...

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Introduction to Conic Sections Conic sections were discovered during the classical Greek period, which lasted from 600 to 300 B.C. By the beginning of the Alexandrian period, enough was known of conics for A pollonius (262–190 B.C.) to produce an eight-volume work on the subject. Conic section, also called conic, in geometry, any curve produced by the intersection of a plane and a right circular cone.Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola.

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CONIC SECTIONS 239 In the following sections, we shall obtain the equations of each of these conic sections in standard form by defining them based on geometric properties. Fig 11. 8 Fig 11. 9 1. 10 11.3 Circle Definition 1 A circle is the set of all points in a plane that are equidistant from a fixed point in the plane. conic sections conics. GOAL 1 10.6 Graphing and Classifying Conics 623 Write and graph an equation of a parabola with its vertex at (h,k) and an equation of a circle, ellipse, or hyperbola with its center at (h, k). Classify a conic using its equation, as applied in Example 8. In the following equations the point (To model real-life situations ...

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Dec 12, 2019 · Download NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections शंकु परिच्छेद in PDF form. Students can do directly 12th class after doing 10th though NIOS Admission 2019-2020. Conic section, also called conic, in geometry, any curve produced by the intersection of a plane and a right circular cone.Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola. 1 CHAPTER 2 CONIC SECTIONS 2.1 Introduction A particle moving under the influence of an inverse square force moves in an orbit that is a conic section; that is to say an ellipse, a parabola or a hyperbola.

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This will be your complete guide to conic sections—what they are, how you'll see them on the test, and the best way to approach these types of ACT math questions. What Are Conic Sections? A conic section is any intersection of a cone (a three dimensional figure) and a plane (a flat, infinite surface).

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