# Conics Polar Equations!

1. Jul 29, 2009

### r34racer01

1. The problem statement, all variables and given/known data
Hyperbola formula 9x^2 - 4y^2 + 36x + 24y - 36 = 0.
Convert to rectangular form, find coordinates of the vertices, find coordinates of the foci, find eccentricity, what is the equation of the conic section in polar coordinates if the pole is taken to be the leftmost focus? Sketch.

2. Relevant equations
a^2 +b^2 = c^2 directrix: x = (a^2)/c e = c/a

3. The attempt at a solution
So I have the hyperbola formula 9x^2 - 4y^2 + 36x + 24y - 36 = 0 I converted it to...
((x+2)^2)/4 - ((y-3)^2)/9 = 1
The vertices I have as (0,3) and (-4,3)
The foci I have as (-2+ sq. root 13,3) and (-2 + sq. root 13, 3)
Eccentricity is (sq. root 13)/2
Now here's the problem I'm having issues trying to find the directrix. I found a formula that says its x = (a^2)/c so after plugging in I get 1.109 but that's between the right vertex and right focus, aren't the directrixes suppose to be between the center and the vertices. Also I'm not quite sure what to do "the pole is taken to be the leftmost focus."

Last edited: Jul 29, 2009