The lengths of tangents from a fixed point to three circles of coaxial system are ${t_1},{t_2},{t_3}$ and if $P, Q$ and $R$ be the centres, then $QRt_1^2 + RPt_2^2 + PQt_3^2$ is equal to

The intercept on the line $y = x$ by the circle ${x^2} + {y^2} – 2x = 0$ is $AB$ . Equation of the circle with $AB$ as a diameter is

Let the mirror image of a circle $c_{1}: x^{2}+y^{2}-2 x-$ $6 y+\alpha=0$ in line $y=x+1$ be $c_{2}: 5 x^{2}+5 y^{2}+10 g x$ $+10 f y +38=0$. If $r$ is the radius of circle $c _{2}$, then $\alpha+6 r^{2}$ is equal to$…..$

The radical axis of the pair of circle ${x^2} + {y^2} = 144$ and ${x^2} + {y^2} – 15x + 12y = 0$ is

The equation of the circle passing through the point $(1, 2)$ and through the points of intersection of $x^2 + y^2 – 4x – 6y – 21 = 0$ and $3x + 4y + 5 = 0$ is given by