Explanation Rearrange the given equation of the parabola as below. x 2 + y = 100 x 2 = 100 − y x 2 = − ( y − 100 ) (1) The general equation of the parabola is ( x − h ) 2 = 4 p ( y − k ) (2) It is given that the ellipse and the parabola shares the vertex and focus. From the equation (1) and (2), it is observed that the vertex of the parabola is ( 0 , 100 ) and hence, one of the vertices of the ellipse is ( 0 , 100 ) . Compare equation (1) and (2). 4 p = − 1 p = − 1 4 The shared focus of the parabola is at the point ( h , k + p ) = ( 0 , 100 − 1 4 ) , that is, ( h , k + p ) = ( 0 , 399 4 ) . It is also given that one of vertex of the ellipse is at ( 0 , 0 ) and it is known that the mid-point of the foci is the center of the ellipse. Thus, 2 c = 399 4 c = 399 8 Therefore, the center of the ellipse is ( 0 , 399 8 ) . The length of the major axis is given by, a = 100 − 399 8 = 800 − 399 8 a = 401 8 Use c 2 = a 2 − b 2 to obtain the value of b as, ( 399 8 ) 2 = ( 401 8 ) 2 − b 2 b 2 =

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ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

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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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Solution Summary: The author compares the equations of the ellipse and the parabola.

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