The equation of the transverse and conjugate axis of the hyperbola $16{x^2} - {y^2} + 64x + 4y + 44 = 0$ are
$x = 2,\;y + 2 = 0$
$x = 2,\;y = 2$
$y = 2,\;x + 2 = 0$
None of these
Length of latusrectum of curve $xy = 7x + 5y$ is
The eccentricity of the hyperbola $5{x^2} - 4{y^2} + 20x + 8y = 4$ is
The locus of middle points of the chords of the circle $x^2 + y^2 = a^2$ which touch the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is
If the two tangents drawn on hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ in such a way that the product of their gradients is ${c^2}$, then they intersects on the curve
The tangent to the hyperbola, $x^2 - 3y^2 = 3$ at the point $\left( {\sqrt 3 \,\,,\,\,0} \right)$ when associated with two asymptotes constitutes :