Consider the circle $x^2+y^2-6x+4y=12$. The equations of a tangent to this circle that is parallel to the line $4x+3y+5=0$ are

Two tangents drawn from $P(1, 7)$ to the circle $x^2 + y^2 = 25$ touch the circle at $Q$ and $R$ respectively. The area of the quadrilateral $PQOR$ is

The circle $x^2+y^2-4x-8y+16=0$ rolls along the tangent drawn to it at $(2+\sqrt{3}, 3)$ by $2$ units. The equation of the circle in the new position is

$A$ circle is such that $(x-2) \cos \theta + (y-2) \sin \theta = 1$ touches it for all values of $\theta$. Then,the circle is

The equation of the normal to a circle at the point $\left( 3 + \frac{3}{\sqrt{2}}, \frac{3}{\sqrt{2}} \right)$ is $y - x + 3 = 0$. To which of the following circles does this normal belong?

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: