If $\frac{{{{\left( {3x - 4y - z} \right)}^2}}}{{100}} - {\frac{{\left( {4x + 3y - 1} \right)}}{{225}}^2} = 1$ then
length of latusrectum of hyperbola is
$4.5$
$\frac{40}{3}$
$9$
$\frac{8}{3}$
Tangents are drawn to the hyperbola $4{x^2} - {y^2} = 36$ at the points $P$ and $Q.$ If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :
The equation of the director circle of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{4} = 1$ is given by
The eccentricity of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{{25}} = 1$ is
The equation of the tangents to the hyperbola $3{x^2} - 4{y^2} = 12$ which cuts equal intercepts from the axes, are
The graph of the conic $ x^2 - (y - 1)^2 = 1$ has one tangent line with positive slope that passes through the origin. the point of tangency being $(a, b). $ Then Eccentricity of the conic is