Posted by Laila on Wednesday, July 30, 2014 at 11:05am.
Sorry it's actually equal to 1 not 0
just make the usual substitution.
y = rsinθ
x = rcosθ
so, that means
r^2sin^2θ/25 - r^2cos^2θ/9 = 1
r^2(9sin^2θ-25cos^2θ) = 225
r^2 = 225/(9sin^2θ-25cos^2θ)
see the expected vertical hyperbola at
http://www.wolframalpha.com/input/?i=plot+r^2+%3D+225%2F%289sin^2%CE%B8-25cos^2%CE%B8%29