How do I find the equation of this hyperbola?
Given:
One focus at (0,25)
Asymptotes intersecting at (0,5)
An asymptote passing through (24,13)

Those are the only given information. (:
Thank you.

Question

How do I find the equation of this hyperbola?
Given:
One focus at (0,25)
Asymptotes intersecting at (0,5)
An asymptote passing through (24,13)

Those are the only given information. (:
Thank you.

anonymous · Answer

do you know the standard form for the equation of a hyperbola?

anonymous · Answer

$$\frac{(x-x_0)^2}{a^2}-\frac{(y-y_0)^2}{b^2}=1$$

anonymous · Answer

since the focus is given above the center (0, 5), the equation should be where the y^2 term is positive...

$\large \frac{(y-y_0)^2}{a^2}-\frac{(x-x_0)^2}{b^2}=1 $

anonymous · Answer

Yes, I know the standard form. :)
Thanks! Now I know the intersection of asymptotes is the center. :)

anonymous · Answer

Hi again, :) I already know that I'll use the equation typed up there ^
But after I substitute 0 and 5 to x0 and y0 in the numerator, what will I do next? :(

anonymous · Answer

I have already solved it.  Thanks for your help! :)