I've been having problems with one particular one. here it is
"Find the equation of the hyperbola if its focuses are $\displaystyle F_1=(10,-2)F_2=(16,2)$ and $\displaystyle 2a=24$.
Any help is greatly appreciated
Regards,
Rinor
I've been having problems with one particular one. here it is
"Find the equation of the hyperbola if its focuses are $\displaystyle F_1=(10,-2)F_2=(16,2)$ and $\displaystyle 2a=24$.
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:
$\displaystyle |\overline{PF_1}| - |\overline{PF_2}| = 2a$
But I hope for you that the original question reads:
"Find the equation of the hyperbola if its focuses are $\displaystyle F_1={\bold{(-10,2)}},~F_2=(16,2)$ and $\displaystyle 2a=24$.
If so:
1. The center is at C(3, 2)
2. e = 13
3. From $\displaystyle e=\sqrt{a^2+b^2}$ follows b = 5
4. The equation of the hyperbola is: ....... $\displaystyle \dfrac{(x-3)^2}{144}-\dfrac{(y-2)^2}{25}=1$