Explanation Approach: Shift 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 . The standard equation of hyperbola is given as, x 2 a 2 − y 2 b 2 = 1 Calculation: The foci F 1 ( 1 , − 5 ) and F 2 ( 1 , 5 ) is lie on the vertical axis, so equation has the form, y 2 a 2 − x 2 b 2 = 1 Replace x by x − h , and y by y − k . ( y − k ) 2 a 2 − ( x − h ) 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 , 1 for x 2 , − 5 for y 1 , and 5 for y 2 in the above center formula. ( h , k ) = ( 1 + 1 2 , − 5 + 5 2 ) = ( 1 , 0 ) Compare the coordinate of foci with ( h , k ± c ) . So, h = 1 k + c = 5 k − c = − 5 The value of k is k = 0

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Chapter 12.4, Problem 41E

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

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Chapter 12.4, Problem 40E

Chapter 12.4, Problem 42E

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

Solution Summary: The author explains the equation of a shifted conic for hyperbola with foci F_1(1,-5) and

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To find:

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

Want to see the full answer?

Chapter 12 Solutions

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

Solution Summary: The author explains the equation of a shifted conic for hyperbola with foci F_1(1,-5) and

Videos

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

Want to see the full answer?

Chapter 12 Solutions

To find:

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