Write the Word or Phrase That Best Completes Each Statement $\mathrm { F } ^ { \prime } ( - \mathrm { c } , 0 )$

question 24

Multiple Choice

Write the word or phrase that best completes each statement or answers the question.
-It can be shown that a hyperbola with center at the origin, foci at $\mathrm { F } ^ { \prime } ( - \mathrm { c } , 0 )$ and $\mathrm { F } ( \mathrm { c } , 0 )$ , and equation $d \left( P , F ^ { \prime } \right) - d ( P , F ) = 2 a$ has equation $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ . Use this result to find an equation of a hyperbola with center at the origin, foci at $( - 6,0 )$ and $( 6,0 )$ , and absolute value of the distances from any point of the hyperbola to the two foci equal to 6 .

• A) \(x ^ { 2 } - y ^ { 2 } = 6\)
• B) \(\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 } = 1\)
• C) \(\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 45 } = 1\)
• D) \(\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 6 } = 1\)

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