The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$,if

The equation of the tangent to the circle $x^2 + y^2 = r^2$ at the point $(a, b)$ is $ax + by - \lambda = 0$,where $\lambda$ is:

If $y=3x$ is a tangent to a circle with centre $(1,1)$,then the other tangent drawn through $(0,0)$ to the circle is

$A$ tangent $PT$ is drawn to the circle $x^2 + y^2 = 4$ at the point $P(\sqrt{3}, 1)$. $A$ line $L$ perpendicular to $PT$ is a tangent to the circle $(x - 3)^2 + y^2 = 1$. Find the common tangent to the two circles.

The line $lx + my + n = 0$ will be a tangent to the circle $x^2 + y^2 = a^2$ if

The tangent to the circle $x^2 + y^2 = 10$ at the point $(3, 1)$ touches the circle $x^2 + y^2 - 2\sqrt{10}x - 20y + k = 0$. Find the value of $k$.