Explanation Given: The vertices of the ellipse are ( − 6 , 2 ) , ( 0 , 2 ) , ( − 3 , − 4 ) and ( − 3 , 8 ) . Formula used: The standard form of the ellipse with its center at ( h , k ) , the length of its axis are 2 a and 2 b : ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 Coordinate of the midpoint of line connecting ( x 1 , y 1 ) and ( x 2 , y 2 ) are ( x 1 + x 2 2 , y 1 + y 2 2 ) . The distance ( d ) between points ( x 1 , y 1 ) and ( x 2 , y 2 ) : d = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 Calculation: Consider the vertices of the ellipse, ( − 6 , 2 ) , ( 0 , 2 ) , ( − 3 , − 4 ) and ( − 3 , 8 ) Form observation, it can be concluded that the axis of the ellipse are parallel to x and y axis because the points lies on the lines parallel to x and y axis. Now, the midpoints of the line connecting ( − 6 , 2 ) and ( 0 , 2 ) and line connecting ( − 3 , − 4 ) and ( − 3 , 8 ) both are the same and the point is the center of the ellipse. Therefore, the center of the ellipse is ( − 6 + 0 2 , 2 + 2 2 ) or ( − 3 + ( − 3 ) 2 , ( − 4 ) + 8 2 ) that is ( − 3 , 2 )

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Author: John Tobey, Jeffrey Slater

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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 9.3, Problem 28E

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To calculate: The equation of the ellipse whose vertices are (−6,2),(0,2),(−3,−4) and (−3,8).

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Chapter 9.3, Problem 27E

Chapter 9.3, Problem 29E

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The equation of the ellipse whose vertices are ( − 6 , 2 ) , ( 0 , 2 ) , ( − 3 , − 4 ) and ( − 3 , 8 ) .

Solution Summary: The author calculates the equation of the ellipse whose vertices are (-6,2), 'left' (0,2), "" (-3,4), and

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To calculate: The equation of the ellipse whose vertices are (−6,2),(0,2),(−3,−4) and (−3,8).

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Chapter 9 Solutions