Question

Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).

Answer 1

The hyperbola is vertical so the equation is gonna be in the form of:
\[(y^2/a^2) -(x^2/b^2) = 1\]

Answer 2

we know a (2) and we know c (11)

Answer 3

so you can use the pythagorean theorem to find b:
a^2 + b^2 = c^2
2^2 + b^2 = 11^2
4 + b^2 = 121
b^2 = 117

Answer 4

so the equation would be:
(y^2/4) - (x^2/117) = 1