The point of contact of the tangent $y = x + 2$ to the hyperbola $5{x^2} - 9{y^2} = 45$ is

The product of the lengths of perpendiculars drawn from any point on the hyperbola $x^2 -2y^2 -2=0$  to its asymptotes is 

The locus of a point $P(\alpha ,\,\beta )$ moving under the condition that the line $y = \alpha x + \beta $ is a tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is

The one which does not represent a hyperbola is

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}}} = $

What will be equation of that chord of hyperbola $25{x^2} - 16{y^2} = 400$, whose mid point is $(5, 3)$