The line $ax + by + c = 0$ is a normal to the circle $x^2 + y^2 = r^2$. The length of the intercept made by the circle on the line $ax + by + c = 0$ is:

If the normals of the parabola $y^2 = 4x$ drawn at the end points of its latus rectum are tangents to the circle $(x - 3)^2 + (y + 2)^2 = r^2$,then the value of $r^2$ is

The area of the triangle formed by the tangent and the normal drawn at $(1, \sqrt{3})$ to the circle $x^2 + y^2 = 4$ and the positive $x$-axis 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 equations of the two tangents from $(-5, -4)$ to the circle $x^{2}+y^{2}+4x+6y+8=0$ are

What is the equation of the tangent to the curve $x^2 + y^2 = a^2$ at the point $\left( \frac{a}{\sqrt{2}}, \frac{a}{\sqrt{2}} \right)$?