The latus rectum of the hyperbola $9{x^2} - 16{y^2} - 18x - 32y - 151 = 0$ is
$\frac{9}{4}$
$9$
$\frac{3}{2}$
$\frac{9}{2}$
The equation of a common tangent to the conics $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ and $\frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}} = 1$ is
Let $P$ is a point on hyperbola $x^2 -y^2 = 4$ , which is at minimum distance from $(0,-1)$ then distance of $P$ from $x-$ axis is
Eccentricity of the curve ${x^2} - {y^2} = {a^2}$ is
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 Length of the latus rectum of the conic is
What is the slope of the tangent line drawn to the hyperbola $xy = a\,(a \ne 0)$ at the point $(a, 1)$