The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$,if

The equation of the normal to the circle $x^2+y^2-2x+4y-5=0$ at the point $(2,1)$ is:

The equations of the tangents to the circle $x^2+y^2=4$ drawn from the point $(4,0)$ are

The line $(x - a)\cos \alpha + (y - b)\sin \alpha = r$ will be a tangent to the circle $(x - a)^2 + (y - b)^2 = r^2$:

The equation of the tangent to the circle at the point $(1, -1)$,whose center is the point of intersection of the straight lines $x - y = 1$ and $2x + y = 3$,is:

The gradient of the normal at the point $(-2, -3)$ on the circle $x^2 + y^2 + 2x + 4y + 3 = 0$ is