The slope of the tangent at the point $(h, h)$ of the circle $x^2 + y^2 = a^2$ is

The equation of the normal to the circle $x^2+y^2=16$ at the point $\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$ is

Suppose two tangents $PA$ and $PB$ are drawn to the circle centered at $C(1, 2)$ from the point $P(16, 7)$. If the area of the quadrilateral $PACB$ is $75$ square units,then the radius of the circle is:

If a circle,whose centre is $(-1, 1)$,touches the straight line $x + 2y + 12 = 0$,then the coordinates of the point of contact are

If the angle between the pair of tangents drawn to the circle $x^2+y^2-2x+4y+3=0$ from the point $(6,-5)$ is $\theta$,then $\cot \theta=$

When are the tangents drawn from the origin to the circle $x^2 + 2px + y^2 - 2qy + q^2 = 0$ perpendicular to each other?