Equation of the normal to the hyperbola $\frac{{{x^2}}}{{25}} - \frac{{{y^2}}}{{16}} = 1$ perpendicular to the line $2x + y = 1$ is
$\sqrt {21} \left( {x - 2y} \right) = 41$
$x - 2y =1$
$\sqrt {41} \left( {x - 2y} \right) = 41$
$\sqrt {21} \left( {x - 2y} \right) = 21$
If area of quadrilateral formed by tangents drawn at ends of latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is equal to square of distance between centre and one focus of hyperbola, then $e^3$ is ($e$ is eccentricity of hyperbola)
The locus of the point of intersection of the lines $bxt - ayt = ab$ and $bx + ay = abt$ is
The eccentricity of the conjugate hyperbola of the hyperbola ${x^2} - 3{y^2} = 1$, is
The coordinates of the foci of the rectangular hyperbola $xy = {c^2}$ are
The locus of a point $P(\alpha ,\,\beta )$ moving under the condition that the line $y = \alpha x + \beta $ is a tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is