Equation of Hyperbola — Help!!

Question

Hi! please help me!

Question:

A light on a wall produces a shadow in the shape of a hyperbola. If the distance between the two vertices of the hyperbola is 10 inches and the distance between the two foci is 12 inches, find the equation of the hyperbola.

Answer needs to be “the equation of the hyperbola formed by the shadow of the light is.......”

Answer 1

Standard equation of hyperbola is

(x/a)^2 - (y/b)^2 = 1 here (a, 0) and (-a, 0) are vertices and asymptotes y = ± ±(b/a)x

Foci are (c, 0) & (-c, 0) then a^2 + b^2 = c^2

In our example 2a = 10 and 2c = 12. Therefore a = 5 and c = 6

Substituting a and c in Pythagorean identity b^2 = 11

Then equation of hyperbola is

(x/5)^2 - y^2/11 = 1

I hope this help.