Finding equation of hyperbola from known coordinates of focii

Quote:

Originally Posted by Rinor Berisha

I've been having problems with one particular one. here it is
"Find the equation of the hyperbola if its focuses are $F_1=(10,-2)F_2=(16,2)$ and $2a=24$ .

Any help is greatly appreciated

Regards,
Rinor

The only way I found is: Use the definition of the hyperbola.

Let P denote any arbitrary point on the hyperbola. Then the equation must be true:

$|\overline{PF_1}| - |\overline{PF_2}| = 2a$

But I hope for you that the original question reads:

"Find the equation of the hyperbola if its focuses are $F_1={\bold{(-10,2)}},~F_2=(16,2)$ and $2a=24$ .

If so:
1. The center is at C(3, 2)
2. e = 13
3. From $e=\sqrt{a^2+b^2}$ follows b = 5
4. The equation of the hyperbola is: ....... $\dfrac{(x-3)^2}{144}-\dfrac{(y-2)^2}{25}=1$