The equations of the tangents to the circle $x^{2}+y^{2}=13$ at the points whose abscissa is $2$ are:

Let $O$ be the origin and $OP$ and $OQ$ be the tangents to the circle $x^2+y^2-6x+4y+8=0$ at the points $P$ and $Q$ on it. If the circumcircle of the triangle $OPQ$ passes through the point $(\alpha, \frac{1}{2})$,then a value of $\alpha$ is

The tangent to the parabola $y = x^2 + 6$ at the point $(1, 7)$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at which point?

Let the tangents at the points $A (4, -11)$ and $B (8, -5)$ on the circle $x^2 + y^2 - 3x + 10y - 15 = 0$ intersect at the point $C$. Then the radius of the circle,whose center is $C$ and the line joining $A$ and $B$ is its tangent,is equal to

The line $ax + by + c = 0$ is normal to the circle $x^2 + y^2 + 2gx + 2fy + d = 0$ if

The angle between the two tangents drawn from the origin to the circle $x^2+y^2-14x+2y+25=0$ is (in $^{\circ}$)