If the length of the transverse and conjugate axes of a hyperbola be $8$ and $6$ respectively, then the difference focal distances of any point of the hyperbola will be

Curve $xy = {c^2}$ is said to be

Area of the triangle formed by the lines $x -y = 0, x + y = 0$ and any tangent to the hyperbola $x^2 -y^2 = a^2$ is :-

The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$

A line parallel to the straight line $2 x-y=0$ is tangent to the hyperbola $\frac{x^{2}}{4}-\frac{y^{2}}{2}=1$ at the point $\left(x_{1}, y_{1}\right) .$ Then $x_{1}^{2}+5 y_{1}^{2}$ is equal to 

The foci of a hyperbola are $( \pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line $2 x+3 y=6$, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the $x$ - and $y$-axes are $a$ and $b$ respectively, then $|6 a|+|5 b|$ is equal to $..........$.