Tangent and Normal to a Hyperbola

The maximum number of normals to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ from an external point is :

Find the equation(s) of the tangent to the hyperbola $2x^2-3y^2=6$ which is parallel to the line $y=x+5$.

Let $P(2,6)$ be a point on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=-1$, if normal at point $P$ meets the hyperbola again at $Q$. Find the coordinates of $Q$.

Let $P(2,6)$ be a point on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=-1$, if normal at point $P$ meets the hyperbola again at $Q$. Find the coordinates of $Q$.

Let $P(-2,-6)$ be a point on the hyperbola $\frac{x^2}{{12}^2}-\frac{y^2}{{12}^2}=-1$, if normal at point $P$ meets the hyperbola again at $Q$. Find the coordinates of $Q$.

Let $P(2,-6)$ be a point on the hyperbola $\frac{x^2}{{12}^2}-\frac{y^2}{{12}^2}=-1$, if normal at point $P$ meets the hyperbola again at $Q$. Find the coordinates of $Q$.

Let $P(2,6)$ be a point on the hyperbola $\frac{x^2}{{12}^2}-\frac{y^2}{{12}^2}=-1$, if normal at point $P$ meets the hyperbola again at $Q$. Find the coordinates of $Q$.

The number of real tangents can be drawn from the point $(16,-3)$ to hyperbola $\frac{x^2}{8}-\frac{y^2}{3}=1$ is

Find the equation(s) of the tangent to the hyperbola $4x^2-3y^2=12$ which is parallel to the line $y=2x+3$.

Find the equation(s) of the tangent to the hyperbola $2x^2-3y^2=24$ which is parallel to the line $y=2x+3$.

Find the equation(s) of the tangent to the hyperbola $2x^2-3y^2=18$ which is parallel to the line $y=6x+7$.

Find the equation(s) of the tangent to the hyperbola $2x^2-3y^2=12$ which is parallel to the line $y=4x+5$.

Find the equation(s) of the tangent to the hyperbola $2x^2-3y^2=6$ which is parallel to the line $y=3x+4$.

The number of points from where a pair of perpendicular tangents can be drawn to the hyperbola $x^2{\sec }^2\alpha -y^2{\mathrm{cosec}}^2\alpha =1$, $\alpha \in \left(0, \frac{\mathrm{\pi }}{4}\right)$, is

The straight line $x+y=\sqrt{2} p$ will touch the curve $4x^2-9y^2=36$ , if :

If the line $y=mx+7\sqrt{3}$ is normal to the hyperbola $\frac{x^2}{24}-\frac{y^2}{18}=1$, then a value of $m$ is:

If the tangent and the normal to $x^2-y^2=4$ at a point cut off intercepts $a_1, a_2$ on the $x$-axis respectively and $b_1, b_2$ on the $y$-axis respectively then the value of $a_1{a}_2+b_1{b}_2$ is

The equation of the tangent to the hyperbola $x^2-4y^2=36$  which is perpendicular to the line $x-y+4=\mathrm{0,}$ is

The equation of the normal to the hyperbola $\frac{{\text{x}}^2}{16}-\frac{{\text{y}}^2}{9}=1$ at (-4, 0) is

A hyperbola passes through the point $P\left(\sqrt{2},\sqrt{3}\right)$ and has foci at $\left(\pm 2,0\right)$. Then the tangent to this hyperbola at $P$ also passes through the point