College Algebra CLEP Prep Practice Exam

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Which of the following is the equation of the hyperbola (x-3)^2/9 – (y+2)^2/14 = 1?

(x-3)^2/9 + (y+2)^2/14 = 1
(x-3)^2/9 – (y+2)^2/4 = 1
(x+3)^2/9 – (y-2)^2/14 = 1
(x+3)^2/9 + (y-2)^2/14 = 1

The correct answer is: (x+3)^2/9 – (y-2)^2/14 = 1

The equation of a hyperbola is in the form (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center and a and b are the distances from the center to a point on the x-axis and y-axis, respectively. Option A has the sign of the y-term incorrect, it should be a negative instead of positive. Option B has the a^2 and b^2 values flipped. Option D has both the signs and the a^2 and b^2 values incorrect. Option C is the correct equation as it matches the form of a hyperbola and has the correct values for h, k, a, and b.