For the hyperbola $\frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{\sin ^2 \alpha}=1$, which of the following remains constant when $\alpha$ varies?

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Aicharya · Accepted Answer

$a^2=\cos ^2 \alpha$ and $b^2=\sin ^2 \alpha$ Coordinates of focii are $(\pm a e, 0)$ $	herefore b^2=a^2\left(e^2-1ight) \Rightarrow e=\sec \alpha$. Hence abscissae of foci remain constant when $\alpha$ varies.

For the hyperbola $\frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{\sin ^2 \alpha}=1$, which of the following remains…

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