The angle between the tangents drawn from the origin to the circle $(x - 7)^2 + (y + 1)^2 = 25$ is:

The straight line $x - y - 3 = 0$ touches the circle $x^2 + y^2 - 4x + 6y + 11 = 0$ at the point whose coordinates are

The equation of the tangent to the circle $x^2+y^2=1$,which is perpendicular to the line $y=mx+1$,is:

The area of the triangle formed by the tangent and the normal drawn at $(1, \sqrt{3})$ to the circle $x^2 + y^2 = 4$ and the positive $x$-axis is:

The straight line $x+2y=1$ cuts the $X$-axis at $A$ and the $Y$-axis at $B$. $A$ circle is drawn through $A, B$ and the origin $O(0,0)$. The sum of the perpendicular distances from $A$ and $B$ to the tangent drawn at the origin to the circle $S$ is:

$3x + 4y - 43 = 0$ is a tangent to the circle $S \equiv x^2 + y^2 - 6x + 8y + k = 0$ at a point $P$. If $C$ is the centre of the circle and $Q$ is a point which divides $CP$ in the ratio $-1:2$,then the power of the point $Q$ with respect to the circle $S = 0$ is