Please help in this MATH problem?

Question

Find the equation of the hyperbola which satisfies the given condition

vertices at (3,-3) and (-13, -3), passes through (5,0)

How to solve this step by step

Answer 1

Calculate the center of the hyperbola

(h,k)=((3+(-13))/2,(-3+(-3))/2)=(-5,-3)

Calculate value of a

a=sqrt((-5-(3))^2+(-3-(-3))^2)

  =8

Hyperbola equation,

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

(x-(-5))^2/8^2-(y-(-3))^2/b^2=1

Hyperbola is pass through point  (5,0)

Substitute x=5,y=0

(5-(-5))^2/8^2-(0-(-3))^2/b^2=1

10^2/8^2-(9/b^2)=1

b^2=16

Therefore,the hyper bola eqution is (x-(-5))^2/8^2-(y-(-3))^2/4^2=1