What are the foci of the hyperbola whose equation is the fraction with numerator open paren x minus 6 close paren squared and denominator 16 minus the fraction with numerator open paren y plus 7 close paren squared and denominator 9 is equal to 1 ?

The equation is in the form (x − 6)²/16 − (y + 7)²/9 = 1, so the center is (6, −7) and the hyperbola opens left and right. For a hyperbola, c² = a² + b², giving c² = 16 + 9 = 25 and c = 5. The foci are 5 units left and right of the center: (1, −7) and (11, −7), which is choice B.

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