The center of a hyperbola is (−2,4) , and one vertex is (−2,7) . the slope of one of the asymptotes is 1/2 .

what is the equation of the hyperbola in standard form? ?

Step-by-step explanation:

The equation of a hyperbola is represented by , where (h, k) is the center of the hyperbola.

As per the given condition, h = -2 and k = 4.

Thus, the equation becomes .

One vertex is (-2, 7).

Hence, putting x = -2 and y = 7, we get .

The slope of the asymptote is .

Hence, .

Thus, the equation is .