If $(1,3)$ is the midpoint of a chord of the circle $x^2+y^2-4x-8y+16=0$,then the area of the triangle formed by that chord with the coordinate axes is

The area of the curve $x^2 + y^2 = 2ax$ is

If a line passing through the point $\left( -\sqrt{8}, \sqrt{8} \right)$ and making an angle of $135^{\circ}$ with the $x$-axis intersects the circle $x = 5 \cos \theta, y = 5 \sin \theta$ at points $A$ and $B$,then find the length of the chord $AB$.

If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2+y^2+4x-6y=12$ externally at the point $(1, -1)$,then the radius of $C$ is

If the ratio of the lengths of the tangents drawn from the point $(1, 2)$ to the circles $x^2 + y^2 + x + y - 4 = 0$ and $3x^2 + 3y^2 - x - y + k = 0$ is $4 : 3$,then $k = \dots$

The number of common tangents to two circles $x^2 + y^2 = 4$ and $x^2 + y^2 - 8x + 12 = 0$ is