Tangent and Normal to a Hyperbola

If two tangents can be drawn to the different branches of hyperbola $x^2-9y^2=9$ from the point $\left(\alpha ,\beta \right)$ then $\left(\alpha ,\beta \right)$ can be

Director circle of a hyperbola is $x^2+y^2-4y=0$, one end of transverse axis is $\left(2,0\right)$ then co-ordinates of focus (foci) is/are

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

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

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

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

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

The number of real tangents can be drawn from the point $(-4,-3)$ to hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=-1$.

The number of real tangents can be drawn from the point $(4,3)$ to hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=-1$.

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 $y=3x+4$.