Pre-calculus - Problem solved

[Ranger Mattos]

Find a polar equation for the hyperbola with a focus at the pole and the given polar coordinates at the endpoints of its transverse axis:
(2.4, π/2) and (-12, 3π/2)

I have no idea how to go about this. I could just look it up in the back of the book, but I need to be able to explain it in class. So, um, please help explain this to me.

EDIT: The π is supposed to be pi.

[John Cribati]

I do remember something from Pre-Calc, and how the 4 axes relate to the Pi fractions.


Pi/2|Pi/4
-------
3Pi/4| Pi

Those vertical ones are supposed to be centered :smallfrown:

[Tirian]

Sorry, was confused, am not now.

So, given the endpoints of the transverse axis, you can figure out what is the center of the hyperbola, and from that you can calculate a and c since you also know the coordinates of a focus, and from that you can calculate the eccentricity of the hyperbola. Finally, you need to find an equation for the hyperbola in polar coordinates with a focus at the pole that uses only those values and you're off to the races.

[Ranger Mattos]

Thanks. I did figure it out, sort of. Luckily I didn't get called on to explain the program. I'll ask my teacher before the test, though.