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: The given equation of an ellipse is 49 x 2 + 8 y 2 = 196 . First rewrite the given equation in form of either x 2 a 2 + y 2 b 2 = 1 or x 2 b 2 + y 2 a 2 = 1 as follows. 49 x 2 + 8 y 2 = 196 49 x 2 + 8 y 2 196 = 196 196 ( ∵ Divide by 196 on both side ) 49 x 2 196 + 8 y 2 196 = 1 x 2 4 + 2 y 2 49 = 1 x 2 2 2 + y 2 ( 7 2 ) 2 = 1 So, the equation of the ellipse 49 x 2 + 8 y 2 = 196 can be written as x 2 2 2 + y 2 ( 7 2 ) 2 = 1

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 11E

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The vertices and the foci of the ellipse with the equation 49x2+8y2=196 and to draw the graph of the ellipse.

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Chapter 21.5, Problem 10E

Chapter 21.5, Problem 12E

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The vertices and the foci of the ellipse with the equation 49 x 2 + 8 y 2 = 196 and to draw the graph of the ellipse.

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The vertices and the foci of the ellipse with the equation 49x2+8y2=196 and to draw the graph of the ellipse.

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Chapter 21 Solutions