Mathematics - Hyperbola Question with Solution | TestHub

The hyperbola is defined by the equation:

$$\frac{x^2}{{\cos }^2\alpha }-\frac{y^2}{{\sin }^2\alpha }=1$$

The coordinates of its vertices are $(\pm \cos \alpha ,0)$. The eccentricity of the hyperbola is given by $e=\sqrt{1+\frac{{\sin }^2\alpha }{{\cos }^2\alpha }}=|\sec \alpha |$.

Therefore, the coordinates of the foci are $(\pm 1,0)$, which are independent of $\alpha$. The directrix is .