The eccentricity of the conjugate hyperbola of $16x^2 - 9y^2 - 32x - 36y - 164 = 0$ is:

If $\frac{x^{2}}{36}-\frac{y^{2}}{k^{2}}=1$ is a hyperbola,then which of the following statements can be true?

If the line $lx + my = 1$ is a normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then $\frac{a^2}{l^2} - \frac{b^2}{m^2}$ is equal to

Find the coordinates of the foci and the vertices,the eccentricity,and the length of the latus rectum of the hyperbola $16 x^{2}-9 y^{2}=576$.

The point from which two distinct tangents can be drawn to two different branches of the hyperbola $\frac{x^2}{25} - \frac{y^2}{16} = 1$,but no two different tangents can be drawn to the circle $x^2 + y^2 = 36$,is:

If $P(\theta)$ lies on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ and $S$ and $S^{\prime}$ are the foci of the hyperbola,then $SP \cdot S^{\prime}P =$