The equation of the tangent at the point $(a\sec \theta ,\;b\tan \theta )$ of the conic $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, is
$x{\sec ^2}\theta - y{\tan ^2}\theta = 1$
$\frac{x}{a}\sec \theta - \frac{y}{b}\tan \theta = 1$
$\frac{{x + a\sec \theta }}{{{a^2}}} - \frac{{y + b\tan \theta }}{{{b^2}}} = 1$
None of these
The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{5} = 1$ , meet $x-$ axis and $y-$ axis at $A$ and $B$ respectively. Then $(OA)^2 - (OB)^2$ , where $O$ is the origin, equals
Equation of hyperbola with asymptotes $3x - 4y + 7 = 0$ and $4x + 3y + 1 = 0$ and which passes through origin is
The chord $ PQ $ of the rectangular hyperbola $xy = a^2$ meets the axis of $x$ at $A ; C $ is the mid point of $ PQ\ \& 'O' $ is the origin. Then the $ \Delta ACO$ is :
The eccentricity of the hyperbola conjugate to ${x^2} - 3{y^2} = 2x + 8$ is
If the vertices of a hyperbola be at $(-2, 0)$ and $(2, 0)$ and one of its foci be at $(-3, 0)$, then which one of the following points does not lie on this hyperbola?