Question

Which equation represents a hyperbola with a center at (0,0), a vertex at (0,60), and a focus at (0,-65)

Answer 1

Given that the hyperbola has a center at (0,0), and its vertices and foci are on y-axis. This, the equation of the hyperbola is of the form
x²/a²-y²/b²=-1 (a>0, b>0)
In the equation, vertices are (0, +/-b) .
Thus, 
b=60
Foci (0,+/-√(a²+b²))
thus
√(a²+60²)=65
hence solving for a²
a²=65²-60²
a²=625
a²=25²
hence the equation is:
x²/25²-y²/60²=-1

Answer 2

Answer:

So for everybody in the future, a clarification is d)y^2/60^2 -x^2/25^2=1