For the hyperbola $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{3} = 1$  the incorrect statement is :

The equation of the common tangents to the two hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ are-

The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$

$2.$ Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

$(A)$ $2 x-\sqrt{5} y-20=0$ $(B)$ $2 x-\sqrt{5} y+4=0$

$(C)$ $3 x-4 y+8=0$ $(D)$ $4 x-3 y+4=0$

$2.$ Equation of the circle with $\mathrm{AB}$ as its diameter is

$(A)$ $x^2+y^2-12 x+24=0$ $(B)$ $x^2+y^2+12 x+24=0$

$(C)$ $\mathrm{x}^2+\mathrm{y}^2+24 \mathrm{x}-12=0$ $(D)$ $x^2+y^2-24 x-12=0$

Give hte answer question $1, 2$

If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is

The equation of the normal at the point $(a\sec \theta ,\;b\tan \theta )$ of the curve ${b^2}{x^2} - {a^2}{y^2} = {a^2}{b^2}$ is

If the eccentricity of the standard hyperbola passing, through the point $(4, 6)$ is $2$, then the equation of the tangent to the hyperbola at $(4, 6)$ is