If $L_1, L_2$ and $L_3$ are the chords of contact of the three points $(2,0), (1,-2)$ and $(4,4)$ respectively with respect to the circle $x^2+y^2=3$,then $L_1, L_2$ and $L_3$ are

The distance between the chords of contact of tangents to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ from the origin and the point $(g, f)$ is:

Tangents $AB$ and $AC$ are drawn from the point $A(0, 1)$ to the circle $x^2 + y^2 - 2x + 4y + 1 = 0$. The equation of the circle passing through $A, B,$ and $C$ is

The equation of the circle whose diameter is the common chord of the circles $x^2+y^2-3x+y-10=0$ and $x^2+y^2-x+2y-20=0$ is

If $A, B$ are the points of contact of the tangents drawn from the point $P(-2, -3)$ to the circle $x^2+y^2-8x-10y+5=0$ and the chord $AB$ subtends an angle $\theta$ at $P$,then $\tan \theta =$

$L_1$ and $L_2$ are two common tangents to two circles. If $L_1$ touches the two circles at $A(1, 1)$ and $B(0, 1)$ and $L_2$ touches the two circles at $C\left(\frac{3}{5}, \frac{4}{5}\right)$ and $D\left(-\frac{1}{5}, \frac{7}{5}\right)$,then the equation of the radical axis of the two circles is