Explanation Given: The given equation of the ellipse is, x 2 + 6 x + 4 y 2 − 16 y + 9 = 0 Approach: The standard equation of ellipse whose center is not at origin is, A ( x − h ) 2 + B ( y − k ) 2 = C Here, A , B and C are nonzero real numbers and center is at ( h , k ) . 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. x 2 + 6 x + 4 y 2 − 16 y + 9 = 0 Express the above equation in the standard form by completing the square. x 2 + 6 x + 4 y 2 − 16 y + 9 = 0 ( x 2 + 6 x + 3 2 ) + 4 ( y 2 − 4 y + 2 2 ) = − 9 + 3 2 + 2 2 ( x 2 + 6 x + 9 ) + 4 ( y 2 − 4 y + 4 ) = − 9 + 9 + 4 ( x + 3 ) 2 + 4 ( y − 2 ) 2 = 16 ... ( 1 ) Compare the equation ( 1 ) with the standard equation A ( x − h ) 2 + B ( y − k ) 2 = C . The value of h is − 3 and k is 2 . Thus, the center of the ellipse is ( h , k ) = ( − 3 , 2 ) . To find the horizontal endpoints, substitute 2 for y in equation ( 1 ) . ( x + 3 ) 2 + 4 ( 2 − 2 ) 2 = 16 ( x + 3 ) 2 = 16 x + 3 = ± 4 x = − 3 ± 4 Solve for the two values of x . x = − 3 + 4 = 1 And, x = − 3 − 4 = − 7 Thus, the end points are ( 1 , 2 ) and ( − 7 , 2 ) . To find the vertical endpoints, substitute − 3 for x in equation ( 1 )

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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 22CR

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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 21CR

Chapter 8.CR, Problem 23CR

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Ch. 8.1 - For Problems 110, answer true or false. The graph...Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Prob. 4CQ Ch. 8.1 - Prob. 5CQ Ch. 8.1 - Prob. 6CQ Ch. 8.1 - Prob. 7CQ Ch. 8.1 - Prob. 8CQ Ch. 8.1 - Prob. 9CQ Ch. 8.1 - Prob. 10CQ

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