How do you find the vertex, focus, and directrix of a hyperbola # (y-2)^2 - (x^2)/4 = 1#?
The vertices are at (
The foci are at (
The directrixes are at
The standard form of the equation for a hyperbola with a vertical transverse axis is
Your equation is
The negative sign in front of the
Your graph will look like the one below.
The coordinates of the vertices are (
So your hyperbola has vertices at (
The coordinates of the foci are (
So the foci are at (
The equation for the directrixes is
Your hyperbola looks like this:
(generated by www.wolframalpha.com)