The equation of the tangent to the circle $x^2+y^2=25$ at $(-3, 4)$ is

Point $M$ moves along the circle $(x - 4)^2 + (y - 8)^2 = 20$. It then breaks away from the circle and moves along a tangent to the circle,passing through the point $(-2, 0)$ on the $x$-axis. The coordinates of the point on the circle at which the moving point broke away can be:

The equation of the normal to the circle $x^2+y^2+6x+4y-3=0$ at $(1,-2)$ is

At which point on the $y$-axis is the line $x = 0$ a tangent to the circle $x^2 + y^2 - 2x - 6y + 9 = 0$?

The equation of the normal at $t=\frac{\pi}{2}$ to the curve $x=2 \sin t, y=2 \cos t$ is

When are the tangents drawn from the origin to the circle $x^2 + 2px + y^2 - 2qy + q^2 = 0$ perpendicular to each other?