The equation of the tangent to the circle ${x^2} + {y^2} = {r^2}$ at $(a,b)$ is $ax + by - \lambda = 0$, where $\lambda $ is
${a^2}$
${b^2}$
${r^2}$
None of these
The equation of circle with centre $(1, 2)$ and tangent $x + y - 5 = 0$ is
$x = 7$ touches the circle ${x^2} + {y^2} - 4x - 6y - 12 = 0$, then the coordinates of the point of contact are
Point $M$ moved along the circle $(x - 4)^2 + (y - 8)^2 = 20 $. Then it broke away from it and moving along a tangent to the circle, cuts the $x-$ axis at the point $(- 2, 0)$ . The co-ordinates of the point on the circle at which the moving point broke away can be :
If the centre of a circle is $(-6, 8)$ and it passes through the origin, then equation to its tangent at the origin, is
The gradient of the tangent line at the point $(a\cos \alpha ,a\sin \alpha )$ to the circle ${x^2} + {y^2} = {a^2}$, is