For the hyperbola frac{x^2}{cos^2 alpha} - fr | vedclass

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(B) The given equation of the hyperbola is $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1$. Comparing this with the standard equation $\fr

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Foci

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(B) The given equation of the hyperbola is $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1$. Comparing this with the standard equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,we have $a^2 = \cos^2 \alpha$ and $b^2 = \sin^2 \alpha$. The coordinates of the foci are given by $(\pm ae, 0)$,where $ae = \sqrt{a^2 + b^2}$. Substituting the values,$ae = \sqrt{\cos^2 \alpha + \sin^2 \alpha} = \sqrt{1} = 1$. Thus,the foci are $(\pm 1, 0)$,which are independent of $\alpha$. Therefore,the foci remain constant as $\alpha$ varies.

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

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