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 the ellipse is x 2 100 + y 2 64 = 1 . Convert the equation of the ellipse x 2 100 + y 2 64 = 1 into standard form as follows. x 2 100 + y 2 64 = 1 x 2 10 2 + y 2 8 2 = 1 Clearly, the equation x 2 10 2 + y 2 8 2 = 1 is in the form of x 2 a 2 + y 2 b 2 = 1

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 21.5, Problem 4E

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The vertices and the foci of the ellipse with the equation x2100+y264=1 and to draw the graph of the ellipse.

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Chapter 21.5, Problem 3E

Chapter 21.5, Problem 5E

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The vertices and the foci of the ellipse with the equation x 2 100 + y 2 64 = 1 and to draw the graph of the ellipse.

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The vertices and the foci of the ellipse with the equation x2100+y264=1 and to draw the graph of the ellipse.

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