Find an equation for the hyperbola with vertices at (0,0); assymptotes at y=+\-5/2x. Answer is in the details. I need a little help.

Question

I am getting:

y^2/100 - x^2/4 =1

but the correct answer is:

y^2/100 - x^2/16

How do you solve for for “b” when you don’t know “c”?

c^2-a^2=b^2

How do you get 16? I got the b value from the assymtpote, since (h,k) are (0,0). The a value isn’t 5 though, it’s 10, so could this be a typo on the “correct” answer?

Answer 1

Correct answer y²/10² -x²/4² = 1 has vertices of (0,10) and (0,-10)

with one asymptote y=5x/2 5/2=a/b = 10/4

Your answer y²/10² - x²/2² has a=10 and b=2 but then one asymptote would be y=10x/2 = 5x not 5x/2