Finding the focus points of a hyperbola
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!
$\endgroup$2 Answers
$\begingroup$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 $a^2+b^2=c^2$
$\endgroup$ 2 $\begingroup$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 $\sqrt{a^2 + b^2}$.
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