Question

The center of a hyperbola is (-4,7), and one vertex is (-2,7). The slope of one of the asymptotes is 2. What is the equation of the hyperbola in standard form?

Answer 1

Explanation:

The center and vertex are horizontally aligned.

a = distance between center and vertex = 2

center (h,k)

asymptotes: y = ±(b/a)x + k∓(b/a)h

(x-h)²/a² - (y-k)²/b² = 1

(x+4)²/2² - (y-7)²/4² = 1