Explanation Given: The given equation of the ellipse is, 16 x 2 + y 2 = 64 Approach: The standard equation of the ellipse with center ( 0 , 0 ) is, A x 2 + B y 2 = C Here, A , B and C are nonzero real numbers. The formula to calculate the distance of a line segment with the given endpoints ( x 1 , y 1 ) and ( x 2 , y 2 ) is, d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Here, d is the length of the line segment. Calculation: Consider the given equation of ellipse. 16 x 2 + y 2 = 64 ... ( 1 ) Compare the above equation with A x 2 + B y 2 = C . Thus, the above equation is of the ellipse with center at ( 0 , 0 ) . Find the endpoints of the major and minor axes. Substitute 0 for y to find the x − intercept in equation ( 1 ) . 16 x 2 + ( 0 ) 2 = 64 16 x 2 = 64 x 2 = 4 x = ± 2 Thus, the end points are ( − 2 , 0 ) and ( 2 , 0 ) . Substitute 0 for x to find y − intercept in equation ( 1 ) . 16 ( 0 ) 2 + y 2 = 64 y 2 = 64 y = ± 8 Thus, the end points are ( 0 , − 8 ) and ( 0 , 8 ) . Major axis belongs to the variable with smaller coefficient. In the equation 16 x 2 + y 2 = 64 , y has the smaller coefficient. Thus the major axis is vertical with end points ( 0 , − 8 ) and ( 0 , 8 )

10th Edition

ISBN: 9781285195728

Author: Jerome E. Kaufmann, Karen L. Schwitters

Publisher: Cengage Learning

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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 8.CR, Problem 17CR

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The length of the major axis and the length of the minor axis for the ellipse of given equation.

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Chapter 8.CR, Problem 16CR

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The length of the major axis and the length of the minor axis for the ellipse of given equation.

Solution Summary: The author explains how to find the length of the major and minor axes for the ellipse of a given equation.

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To find: The length of the major axis and the length of the minor axis for the ellipse of given equation.

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To find:

The length of the major axis and the length of the minor axis for the ellipse of given equation.