Question

The hyperbola is horizontal with center at the midpoint (-7,-3) of the foci. A directrix of the hyperbola is y = 0. What is the equation of the hyperbola?

Answer 1

To find the equation of the hyperbola, we need to use the standard form equation for a horizontal hyperbola.

Step-by-step explanation:

To find the equation of the hyperbola, we need to use the standard form equation for a horizontal hyperbola: (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center of the hyperbola and a and b are the lengths of the semi-major and semi-minor axes respectively.

Given that the center of the hyperbola is (-7,-3) and that the foci are located at the same point as the center, we can determine the distance between the center and the foci, which is equal to a. Since the directrix is y = 0, the distance between the center and the directrix is equal to b.

Substituting the values into the standard equation, we can find the equation of the hyperbola.