If a circle with centre at $(-1,1)$ touches the line $x+2 y+4=0$ then the co-ordinates of the point of contact are

A pair of tangents are drawn to the circle $x^2+y^2+6 x-4 y-12=0$ from a point $\mathrm{P}(-4,-5)$, then the area enclosed between these tangents and the area of the circle is

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

Let the circle with centre at origin pass through the vertices of an equilateral triangle ABC . If $A \equiv(2,4)$, then the length of the median through A is