Help with a hyperbola question?
Find an equation in standard form for the hyperbola with vertices at (0, +- 2) and foci at (0, +- 7).

Question

Help with a hyperbola question?
Find an equation in standard form for the hyperbola with vertices at (0, +- 2) and foci at (0, +- 7).

sleepyjess · Answer

@ganeshie8

sleepyjess · Answer

I know that the equation will be $\dfrac{y^2}{a^2} - \dfrac{x^2}{b^2} = 1$, but I'm not sure how to find a and b

ganeshie8 · Answer

Vertices = $(0,~\pm a$)

compare that with given vertices and find $a$

sleepyjess · Answer

So a would be 7!

sleepyjess · Answer

No, 2!

ganeshie8 · Answer

Yes $a=2$,

next use below and find $c$ first
Foci = $(0,\pm c)$

sleepyjess · Answer

c would be 7 :)

ganeshie8 · Answer

use the raltion $a^2+b^2=c^2$ and find $b$

sleepyjess · Answer

$b^2$ would be 45

ganeshie8 · Answer

Yep! plug them in the standard form of equation of vertical hyperbola

sleepyjess · Answer

$\dfrac{y^2}4 - \dfrac{x^2}{45}=1$! "D

sleepyjess · Answer

* :D

ganeshie8 · Answer

sleepyjess · Answer

That was actually a lot easier than I thought it would be :)

ganeshie8 · Answer

it was easy because you remembered the standard form and formulas for vertices and foci :)

sleepyjess · Answer

:) I always overthink math