Question

Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).

Answer 1

equation of hyperbola \[y^2/a^2-x^2/b^2 = 1\]
Put x = 0, y =\[\pm 9\]
\[y^2/a^2-0^2/b^2 = 1\]
\[a= 9\]
using the focal length and the a length we can determine b if need be
\[a^2+b^2 = f^2\]
Now put these values in standard equations