HELP!!!! Center at the origin, Transverse axis at x-axis, distance between foci is 2√97, latus rectum is 32/9

Question

anonymous · Answer

HELP PLEASE!!!

tkhunny · Answer

So, it's an ellipse.
Center at the Origin gives: $\dfrac{x^2}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1$

x-Axis is Transverse (or Major) Axis give:  a > b

Distance between foci gives $c = \sqrt{97}$

Latus Rectum is 32/9 gives $2\cdot\dfrac{b^{2}}{a} = 32/9$

Well, that's all the problem statement gave us.  Now what?

anonymous · Answer

its hyperbola.. hehe wait, 2√97, what happened to 2?

tkhunny · Answer

Well, you shoudl have said so!

c is HALF the distance between the foci.  Just like a is half the length fo the Transverse Axis and b is half the length of the congugate axis.

anonymous · Answer

sorry.. thank you :)

tkhunny · Answer

Change it to -y^2 instead of +y^2, and we're still on the right track.

anonymous · Answer

why is it changed to negative?

tkhunny · Answer

Because it an hyperbola and not an ellipse.

anonymous · Answer

yes yes.

anonymous · Answer

ahm, how to get a and b?