Explanation Approach: Shifting graph of equations If h and k are real numbers, then replacing x by x − h or by x + h and replacing y by y − k or by y + k . Calculation: The foci F 1 ( 1 , − 4 ) and F 2 ( 5 , − 4 ) is lie on the vertical axis, so equation has the form, x 2 a 2 + y 2 b 2 = 1 Replace x by x − h , and y by y − k . ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 …… ( 1 ) The center is midway of the foci so the coordinates of the center will be as follows, ( h , k ) = ( x 1 + x 2 2 , y 1 + y 2 2 ) Substitute 1 for x 1 , 5 for x 2 , − 4 for y 1 , and − 4 for y 2 in the above center formula. ( h , k ) = ( 1 + 5 2 , − 4 − 4 2 ) = ( 6 2 , − 8 2 ) = ( 3 , − 4 ) Compare the coordinate of foci with ( h ± c , k ) . So, h + c = 5 3 + c = 5 c = 5 − 3 = 2 The ellipse passes through the point ( 3 , 1 ) , point x = 3 , and y = 1 must lie on ellipse. Substitute 3 for x , 1 for y , 3 for h , and − 4 for k in equation ( 1 )

4th Edition

ISBN: 8220100548512

Author: Watson

Publisher: CENGAGE L

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Chapter 12.4, Problem 43E

To determine

To find:

The equation of a shifted conic for ellipse with foci F1(1,−4) and F2(5,−4) that passes through the point (3,1).

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Chapter 12.4, Problem 42E

Chapter 12.4, Problem 44E

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Chapter 12 Solutions

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The equation of a shifted conic for ellipse with foci F 1 ( 1 , − 4 ) and F 2 ( 5 , − 4 ) that passes through the point ( 3 , 1 ) .

Solution Summary: The author explains the equation of a shifted conic for ellipse with foci F_1(1,-4) and

To find:

The equation of a shifted conic for ellipse with foci F1(1,−4) and F2(5,−4) that passes through the point (3,1).

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Chapter 12 Solutions

The equation of a shifted conic for ellipse with foci F 1 ( 1 , − 4 ) and F 2 ( 5 , − 4 ) that passes through the point ( 3 , 1 ) .

Solution Summary: The author explains the equation of a shifted conic for ellipse with foci F_1(1,-4) and

To find: The equation of a shifted conic for ellipse with foci F1(1,−4) and F2(5,−4) that passes through the point (3,1).

Want to see the full answer?

Chapter 12 Solutions

To find:

The equation of a shifted conic for ellipse with foci F1(1,−4) and F2(5,−4) that passes through the point (3,1).