What are the vertices of the hyperbola whose equation is the fraction with numerator open paren y plus 6 close paren squared and denominator 81 minus the fraction with numerator open paren x plus 8 close paren squared and denominator 49 is equal to 1 ?

The equation is in the form (y − k)²/a² − (x − h)²/b² = 1, so the hyperbola opens up and down. Its center is (−8, −6), and a² = 81 gives a = 9. The vertices are 9 units above and below the center: (−8, 3) and (−8, −15), which is choice C.

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