The eccentricity of the conic section $x^2 - 4y^2 = 1$ is:

If $2x - ky + 3 = 0$ and $3x - y + 1 = 0$ are conjugate lines with respect to the hyperbola $5x^2 - 6y^2 = 15$,then $k =$

Which of the following equations in parametric form can represent a hyperbola,where $t$ is a parameter?

If $PN$ is the perpendicular from a point $P$ on the rectangular hyperbola $x^2 - y^2 = a^2$ to any of its asymptotes,then the locus of the midpoint of $PN$ is:

Let the domain of the function $f(x) = \log_{3}\log_{5}\log_{7}(9x - x^{2} - 13)$ be the interval $(m, n)$. Let the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ have eccentricity $\frac{n}{3}$ and the length of the latus rectum $\frac{8m}{3}$. Then $b^{2} - a^{2}$ is equal to:

The equation of a tangent to the hyperbola $5x^{2}-y^{2}=5$ which passes through the external point $(2, 8)$ is: