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Provide an Appropriate Response F(c,0)F ^ { \prime } ( - c , 0 )

question 114

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Provide an appropriate response.
-It can be shown that a hyperbola with center at the origin, foci at F(c,0) F ^ { \prime } ( - c , 0 ) and F(c,0) F ( c , 0 ) , and equation d(P,F) d(P,F) =2ad \left( P , F ^ { \prime } \right) - d ( P , F ) = 2 a has equation x2a2y2b2=1\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 . Use this result to find an equation of a hyperbola with center at the origin, foci at (8,0) ( - 8,0 ) and (8,0) ( 8,0 ) , and absolute value of the distances from any point of the hyperbola to the two foci equal to 8 .

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