The slope of the tangent to the circle $x^2 + y^2 = a^2$ at the point $(h, k)$ is:

If $y=3x$ is a tangent to a circle with centre $(1,1)$,then the other tangent drawn through $(0,0)$ to the circle is

The equation of the normal to the circle $x^2 + y^2 = 9$ at the point $\left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right)$ is

The equation of a tangent to the circle $x^2+y^2+2x-12y-132=0$ which is perpendicular to the line $12x+5y+k=0$ is

The line $x + y = 2$ is tangent to the curve $x^2 = 3 - 2y$ at its point

$A$ 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