The equations of the tangents to the circle $x^2+y^2=36$ which are perpendicular to the line $5x+y-2=0$ are

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 $P$.

For what possible value of $p$ is the line $x \cos \alpha + y \sin \alpha = p$ a tangent to the circle $x^2 + y^2 - 2qx \cos \alpha - 2qy \sin \alpha = 0$?

$A$ 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 equations of the tangents to the circle $x^2 + y^2 = 50$ at the points where the line $x + 7 = 0$ meets it,are

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