The equation of the radical axis of the pair of circles $7x^2+7y^2-7x+14y+18=0$ and $4x^2+4y^2-7x+8y+20=0$ is

If $P(\alpha, \beta)$ is the radical centre of the circles $S \equiv x^2+y^2+4x+7=0$,$S^{\prime} \equiv 2x^2+2y^2+3x+5y+9=0$ and $S^{\prime \prime} \equiv x^2+y^2+y=0$,then the length of the tangent drawn from $P$ to $S^{\prime}=0$ is

For what value of $k$ do the circles $x^2 + y^2 + 5x + 3y + 7 = 0$ and $x^2 + y^2 - 8x + 6y + k = 0$ intersect orthogonally?

The two circles $x^2 + y^2 - 2x - 3 = 0$ and $x^2 + y^2 - 4x - 6y - 8 = 0$ are such that:

The centres of all circles passing through the points of intersection of the circles $x^2+y^2+2x-2y+1=0$ and $x^2+y^2-2x+2y-2=0$ and having radius $\sqrt{14}$ lie on the curve

If the circles $x^2+y^2-4x+6y+13-a^2=0$ and $x^2+y^2-10x-2y+17=0$ intersect in two distinct points,then '$a$' is