Explanation Given: The given equation for the ellipse is, 3 x 2 − 12 x + 5 y 2 + 10 y − 10 = 0 Approach: Consider the standard equation of an ellipse, A ( x − h ) 2 + B ( y − k ) 2 = C Here, A , B , C are non-zero real numbers of the same sign and ( h , k ) is center of an ellipse. To find the endpoints for the x -axis, Substitute k for y in the standard equation of an ellipse and solve for x as follows, A ( x − h ) 2 + B ( ( k ) − k ) 2 = C To find the endpoints for y -axis, Substitute h for x in the standard equation of an ellipse equation and solve for y as follows, A ( ( h ) − h ) 2 + B ( y − k ) 2 = C Find the length of major axis as follows, l = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Here, l is the length of major axis, ( x 1 , y 1 ) , ( x 2 , y 2 ) are the points of major axis. Calculation: Consider the given equation of an ellipse, 3 x 2 − 12 x + 5 y 2 + 10 y − 10 = 0 ... ( 1 ) Complete the square on x and on y and rearrange equation ( 1 ) into the standard equation of an ellipse as follows, 3 x 2 − 12 x + 5 y 2 + 10 y − 10 = 0 3 ( x 2 − 4 x ) + 5 ( y 2 + 2 y ) = 10 3 ( x 2 − 4 x ) + 5 ( y 2 + 2 y ) = 10 3 ( x 2 − 4 x + 4 ) + 5 ( y 2 + 2 y + 1 ) = 10 + 12 + 5 Solve further, 3 ( x − 2 ) 2 + 5 ( y + 1 ) = 27 3 ( x − 2 ) 2 + 5 ( y − ( − 1 ) ) = 27 ... ( 2 ) Compare equation ( 2 ) with standard equation A ( x − h ) 2 + B ( y − k ) 2 = C

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ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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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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The length of the major axis for the given ellipse.

Solution Summary: The author explains how to find the length of the major axis for the given ellipse.

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To find:

The length of the major axis for the given ellipse.