The equation of the circle passing through the point $(-2, 4)$ and through the points of intersection of the circle ${x^2} + {y^2} – 2x – 6y + 6 = 0$ and the line $3x + 2y – 5 = 0$, is

Locus of the points from which perpendicular tangent can be drawn to the circle ${x^2} + {y^2} = {a^2}$, is

The value of k so that ${x^2} + {y^2} + kx + 4y + 2 = 0$ and $2({x^2} + {y^2}) – 4x – 3y + k = 0$ cut orthogonally is

If a variable line, $3x + 4y -\lambda  = 0$ is such that the two circles $x^2 + y^2 -2x -2y + 1 = 0$ and $x^2 + y^2 -18x -2y + 78 = 0$ are on its opposite sides, then the set of all values of $\lambda $ is the interval

A circle ${C_1}$ of radius $2$ touches both $x$ – axis and $y$ – axis. Another circle ${C_2}$ whose radius is greater than $2$ touches circle ${C_1}$ and both the axes. Then the radius of circle ${C_2}$ is