The angle between the tangents to the circle $x^2+y^2=25$ from the point $(1,7)$ 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.

$A$ is the centre of the circle $x^2+y^2-2x-4y-20=0$. If the tangents drawn at the points $B(1,7)$ and $D(4,-2)$ on the circle meet at the point $C$,then the area of the quadrilateral $ABCD$ (in square units) is

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

The area of the triangle formed by the positive $X$-axis, the tangent and the normal to the curve $x^2+y^2=16a^2$ at the point $(2\sqrt{2}a, 2\sqrt{2}a)$ is

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: