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:

The value of $c$,for which the line $y = 2x + c$ is a tangent to the circle $x^2 + y^2 = 16$,is

The equation of a line parallel to the line $3x + 4y = 0$ and touching the circle $x^{2} + y^{2} = 9$ in the first quadrant is:

Let $A$ be the center of the circle $x^2 + y^2 - 2x - 4y - 20 = 0$. If $B(1, 7)$ and $D(4, -2)$ are points on the circle,and the tangents at $B$ and $D$ meet at $C$,then the area of the quadrilateral $ABCD$ is:

The line $ax + by + c = 0$ is normal to the circle $x^2 + y^2 + 2gx + 2fy + d = 0$ if

If $P(-9,-1)$ is a point on the circle $x^2+y^2+4x+8y-38=0$,then find the equation of the tangent drawn at the other end of the diameter drawn through $P$.