If the line $y = mx + c$be a tangent to the circle ${x^2} + {y^2} = {a^2}$, then the point of contact is

Let the tan gents drawn to the circle, $x^2 + y^2 = 16$ from the point $P(0, h)$ meet the $x-$ axis at point  $A$ and $B.$ If the area of $\Delta APB$ is minimum, then $h$  is equal to

The equation of the normal to the circle ${x^2} + {y^2} – 2x = 0$ parallel to the line $x + 2y = 3$ is

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

The condition that the line $x\cos \alpha + y\sin \alpha = p$ may touch the circle ${x^2} + {y^2} = {a^2}$ is