Question

8. Find the standard form of the equation of the hyperbola with the given information.

Please help

Answer 1

none of these are correct

Explanation:

asymptote of a hyperbola

y = b/a (x - h) + k and y = -b/a (x - h) + k

our asymptote given is

y = 5/2 (x + 1) - 8 and y = -5/2(x + 1) - 8

b = 5

a = 2

b^2 = 25

a^2 = 4

standard form of hyperbola

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

or

(y - k)^2 / a^2 - ( x - h)^2 / b^2 = 1

plug in our values

(x + 1)^2 / 4 - (y + 8)^2 / 25 = 1

(y + 8)^2 / 4 - (x + 1)^2 / 25 = 1

which match none of the given options, so none of these are correct