The gradient of the tangent line at the point $(a \cos \alpha, a \sin \alpha)$ to the circle $x^2 + y^2 = a^2$ is

The normal to the circle given by $x^2+y^2-6x+8y-144=0$ at $(8,8)$ meets the circle again at the point

The slope of the common tangent drawn to the circles $x^2+y^2-4x+12y-216=0$ and $x^2+y^2+6x-12y+36=0$ is

Let $A$ be 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 given circle meet at the point $C$,then the area of the quadrilateral $ABCD$ is

The equation of the normal to the circle $x^2+y^2-2x+4y-5=0$ at the point $(2,1)$ is:

The point on the curve $x^2+y^2=a^2, y \geq 0$,at which the tangent is parallel to the $x$-axis is