Finding the focus points of a hyperbola

Question

So I have the following hyperbola : $\frac{x^{'2}}{4}-\frac{y^{'2}}{4}=-1$

I need to find the focus points of this hyperbola. What is some analytical way to do this ?

Thank yoU!

Answer 1

Hint:

Your hyperbola has equation: $$ \frac{y^2}{a^2}-\frac{x^2}{b^2}=\frac{y^2}{4}-\frac{x^2}{4}=1 $$ so has foci on the $y$ axis and the ordinates $\pm c$ of the foci are such that $a^2+b^2=c^2$

Answer 2

The hyperbola $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$ is centered at $(0,0)$, oriented with the vertices on the $y$ axis, and the distance from the center to each focus is $\sqrt{a^2 + b^2}$.