The equation of the tangent parallel to $y-x+5=0$ drawn to $\frac{x^{2}}{3}-\frac{y^{2}}{2}=1$ is

If the vertices and foci of a hyperbola are respectively $(\pm 3,0)$ and $(\pm 4,0)$,then the parametric equations of that hyperbola are:

The foci of a hyperbola are $(\pm 2, 0)$ and its eccentricity is $\frac{3}{2}$. $A$ tangent,perpendicular to the line $2x + 3y = 6$,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 $|6a| + |5b|$ is equal to $..........$.

The eccentricity of the conic ${x^2} - 4{y^2} = 1$ is

If the tangent drawn at a point $P(t)$ on the hyperbola $x^2-y^2=c^2$ cuts the $X$-axis at $T$ and the normal drawn at the same point $P$ cuts the $Y$-axis at $N$,then the equation of the locus of the midpoint of $TN$ is

The angle between the tangents drawn from the point $(2\sqrt{2}, 1)$ to the hyperbola $16x^2 - 25y^2 = 400$ is ........