# Finding a Hyperbola w/ 2 given points

1. May 26, 2014

### yopoe

1. The problem statement, all variables and given/known data

Find the equation for a hyperbola centered at the origin with points (-10,3pi/2) and (2,pi/2)

2. Relevant equations

x^2/a^2 -y^2/b^2=1 or y^2/a^2 - x^2/b^2 = 1

* r=ke/(1±ecos(theta))

*cos can be replaced with sin and the ± is either a plus or a minus depending on the directrix

3. The attempt at a solution

I think the second equation is the only one that can be used but I do not know how to solve with that equation without guessing and checking.

Using the first equation I attempted to plug in values for x and y (they did not check out) in the first equation but I am pretty sure that the coordinates are polar coordinates. I am not really sure what to do but if you could point me in the right direction that would be great. Sorry I do not have the original problem so I do not know the question word for word. Any help would be much appreciated.

2. May 26, 2014

### LCKurtz

If those are polar coordinates then they correspond to (0,10) and (0,2) in rectangular coordinates. No hyperbola centered at the origin could pass through both. (Assuming it isn't rotated, and maybe not even then.)

Last edited: May 26, 2014