If the circles ${x^2} + {y^2} - 2ax + c = 0$ and ${x^2} + {y^2} + 2by + 2\lambda = 0$ intersect orthogonally, then the value of $\lambda $ is
$c$
$-c$
$0$
None of these
The equation of radical axis of the circles ${x^2} + {y^2} + x - y + 2 = 0$ and $3{x^2} + 3{y^2} - 4x - 12 = 0,$ is
The circle on the chord $x\cos \alpha + y\sin \alpha = p$ of the circle ${x^2} + {y^2} = {a^2}$ as diameter has the equation
The locus of centre of a circle passing through $(a, b)$ and cuts orthogonally to circle ${x^2} + {y^2} = {p^2}$, is
The condition that the circle ${(x - 3)^2} + {(y - 4)^2} = {r^2}$ lies entirely within the circle ${x^2} + {y^2} = {R^2},$ is
The equation of director circle of the circle ${x^2} + {y^2} = {a^2},$ is