$A$ is the centre of the circle $x^2+y^2-2x-4y-20=0$. If the tangents drawn at the points $B(1,7)$ and $D(4,-2)$ on the circle meet at the point $C$,then the area of the quadrilateral $ABCD$ (in square units) is

The equation of the tangent to the circle $x^2+y^2=1$,which is perpendicular to the line $y=mx+1$,is:

The equations of the tangents drawn from the origin to the circle $x^2+y^2+2gx+2fy+g^2=0$ are

Two tangents are drawn from a point $P$ to the circle $x^{2}+y^{2}-2x-4y+4=0$,such that the angle between these tangents is $\tan^{-1}\left(\frac{12}{5}\right)$,where $\tan^{-1}\left(\frac{12}{5}\right) \in (0, \pi)$. If the centre of the circle is denoted by $C$ and these tangents touch the circle at points $A$ and $B$,then the ratio of the areas of $\Delta PAB$ and $\Delta CAB$ is:

Let the equation of a circle be $x^{2}+y^{2}-6x-4y+9=0$. Then the line $4x+3y-8=0$ is a

The line $3x - 2y = k$ meets the circle ${x^2} + {y^2} = 4{r^2}$ at only one point,if ${k^2} =$