The length of the transverse axis of a hyperbola is $7$ and it passes through the point $(5, -2)$. The equation of the hyperbola is
$\frac{4}{{49}}{x^2} - \frac{{196}}{{51}}{y^2} = 1$
$\frac{{49}}{4}{x^2} - \frac{{51}}{{196}}{y^2} = 1$
$\frac{4}{{49}}{x^2} - \frac{{51}}{{196}}{y^2} = 1$
None of these
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $9 y^{2}-4 x^{2}=36$
The locus of the midpoints of the chord of the circle, $x^{2}+y^{2}=25$ which is tangent to the hyperbola $, \frac{ x ^{2}}{9}-\frac{ y ^{2}}{16}=1$ is
Eccentricity of the rectangular hyperbola $\int_0^1 {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^3}}}} \right)} \;dx$ is
The tangent to the hyperbola, $x^2 - 3y^2 = 3$ at the point $\left( {\sqrt 3 \,\,,\,\,0} \right)$ when associated with two asymptotes constitutes :
If the tangent and normal to a rectangular hyperbola $xy = c^2$ at a variable point cut off intercept $a_1, a_2$ on $x-$ axis and $b_1, b_2$ on $y-$ axis, then $(a_1a_2 + b_1b_2)$ is