If the latus rectum of an hyperbola be 8 and eccentricity be $3/\sqrt 5 $, then the equation of the hyperbola is
$4{x^2} - 5{y^2} = 100$
$5{x^2} - 4{y^2} = 100$
$4{x^2} + 5{y^2} = 100$
$5{x^2} + 4{y^2} = 100$
If two points $P$ and $Q$ on the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ whose centre is $C$, are such that $CP$ is perpendicular to $CQ, ( a < b )$ , then value of, $\frac{1}{{{{(CP)}^2}}} + \frac{1}{{{{(CQ)}^2}}} = $
If a circle cuts a rectangular hyperbola $xy = {c^2}$ in $A, B, C, D$ and the parameters of these four points be ${t_1},\;{t_2},\;{t_3}$ and ${t_4}$ respectively. Then
For hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} - \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 1$ which of the following remains constant with change in $'\alpha '$
For the hyperbola $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{3} = 1$ the incorrect statement is :