Length of latusrectum of curve $xy = 7x + 5y$ is
$\sqrt {280}$
$\sqrt {225}$
$\sqrt {180}$
$\sqrt {325}$
The equation of the hyperbola whose foci are $(-2, 0)$ and $(2, 0)$ and eccentricity is $2$ is given by :-
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
The eccentricity of the hyperbola $5{x^2} - 4{y^2} + 20x + 8y = 4$ is
The equation of a tangent to the hyperbola $4x^2 -5y^2 = 20$ parallel to the line $x -y = 2$ is
The eccentricity of curve ${x^2} - {y^2} = 1$ is