The equation of the tangents to the conic $3{x^2} - {y^2} = 3$ perpendicular to the line $x + 3y = 2$ is
$y = 3x \pm \sqrt 6 $
$y = 6x \pm \sqrt 3 $
$y = x \pm \sqrt 6 $
$y = 3x \pm 6$
The eccentricity of the hyperbola can never be equal to
The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is $16$ and eccentricity is $\sqrt 2 $, is
A hyperbola passes through the point $P\left( {\sqrt 2 ,\sqrt 3 } \right)$ has foci at $\left( { \pm 2,0} \right)$. Then the tangent to this hyperbola at $P$ also passes through the point
Eccentricity of the rectangular hyperbola $\int_0^1 {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^3}}}} \right)} \;dx$ is
The length of transverse axis of the parabola $3{x^2} - 4{y^2} = 32$ is