Explanation Definition used: Equation of an ellipse with center at ( 0 , 0 ) , and major axis along x-axis: “An equation of the ellipse with center at ( 0 , 0 ) , foci at ( ± c , 0 ) ( 0 , ± c ) , ends of the minor axis at ( 0 , ± b ) and vertices at ( ± a , 0 ) is x 2 a 2 + y 2 b 2 = 1 where a > b > 0 and b 2 = a 2 − c 2 .” Equation of an ellipse with center at ( 0 , 0 ) , and major axis along y-axis: “An equation of the ellipse with center at ( 0 , 0 ) , foci at ( 0 , ± c ) , ends of the minor axis at ( ± b , 0 ) and vertices at ( 0 , ± a ) is x 2 b 2 + y 2 a 2 = 1 where a > b > 0 and b 2 = a 2 − c 2 .” Calculation: Given that the center is at ( 0 , 0 ) , passing through the point ( 2 , 3 ) , vertex at ( 8 , 0 ) . Note that the vertex is of the form ( a , 0 ) . As the focus lies on the positive x -axis, the major axis is along the x -axis. This implies that a = 8 . Thus, the equation of the ellipse is of the form, x 2 a 2 + y 2 b 2 = 1 where a 2 = 64

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 21.5, Problem 23E

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The equation of an ellipse with center at (0,0), passing through the point (2,3), vertex at (8,0).

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Chapter 21.5, Problem 22E

Chapter 21.5, Problem 24E

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The equation of an ellipse with center at ( 0 , 0 ) , passing through the point ( 2 , 3 ) , vertex at ( 8 , 0 ) .

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The equation of an ellipse with center at (0,0), passing through the point (2,3), vertex at (8,0).

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Chapter 21 Solutions