What are the foci of the hyperbola whose equation is the fraction with numerator open paren y minus 2 close paren squared and denominator 64 minus the fraction with numerator open paren x minus 4 close paren squared and denominator 36 is equal to 1 ?

The equation is in the form of a vertical hyperbola centered at (4, 2), with a² = 64 and b² = 36. For a hyperbola, c² = a² + b², so c² = 100 and c = 10. The foci are 10 units above and below the center: (4, 12) and (4, −8), which is choice D.

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