The Cartesian form of the curve given by $x = \frac{a}{2} (t + \frac{1}{t})$ and $y = \frac{a}{2} (t - \frac{1}{t})$,where $t$ is a parameter,is:

If $e_1$ is the eccentricity of the ellipse $\frac{x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of a hyperbola passing through the foci of the given ellipse and $e_1 e_2=1$,then the equation of such a hyperbola among the following is

The length of the conjugate axis of a hyperbola is greater than the length of the transverse axis. Then, the eccentricity $e$ is

Find the equations of the tangent and normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ at the point $(x_{0}, y_{0})$.

The foci of the hyperbola $4x^2 - 9y^2 - 36 = 0$ are:

The tangent to the hyperbola $x^2 - 3y^2 = 3$ at the point $(\sqrt{3}, 0)$ when associated with its two asymptotes constitutes: