Explanation Formula used: 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 ) and ( 0 , c ) , and vertices at ( 0 , − a ) and ( 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 ) , focus is at ( 0 , 1 ) and vertex at ( 0 , − 2 ) . Note that the focus is of the form ( 0 , c ) . As the focus lies on the positive y -axis, the major axis is along the y -axis. Then the values of a and c are 2 and 1, respectively. Thus, the equation of the ellipse is of the form, x 2 b 2 + y 2 a 2 = 1 where a = 2 and c = 1

11th Edition

ISBN: 9780135163078

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 11.3, Problem 30AYU

To determine

The equation of an ellipse with center at (0,0), focus at (0,1), vertex at (0,−2) and then sketch the graph of the ellipse.

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Chapter 11.3, Problem 29AYU

Chapter 11.3, Problem 31AYU

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Chapter 11 Solutions

Algebra And Trigonometry (11th Edition)

Ch. 11.2 - Prob. 1AYU Ch. 11.2 - Prob. 2AYU Ch. 11.2 - Prob. 3AYU Ch. 11.2 - Prob. 4AYU Ch. 11.2 - Prob. 5AYU Ch. 11.2 - Prob. 6AYU Ch. 11.2 - Prob. 7AYU Ch. 11.2 - Prob. 8AYU Ch. 11.2 - Prob. 9AYU Ch. 11.2 - Prob. 10AYU

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The equation of an ellipse with center at ( 0 , 0 ) , focus at ( 0 , 1 ) , vertex at ( 0 , − 2 ) and then sketch the graph of the ellipse.

The equation of an ellipse with center at (0,0), focus at (0,1), vertex at (0,−2) and then sketch the graph of the ellipse.

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Chapter 11 Solutions