The value of $\lambda$,for which the circle $x^2 + y^2 + 2\lambda x + 6y + 1 = 0$ intersects the circle $x^2 + y^2 + 4x + 2y = 0$ orthogonally is

The equation of the circle described on the chord $3x + y + 5 = 0$ of the circle $x^2 + y^2 = 16$ as diameter is:

The equation of a circle which touches the straight lines $x+y=2$,$x-y=2$ and also touches the circle $x^2+y^2=1$ is

If the equation of the circle passing through the points of intersection of the circles $S_1: x^2 - 2x + y^2 - 4y - 4 = 0$ and $S_2: x^2 + 2x + y^2 + 4y - 4 = 0$ passes through the point $(3, 3)$,and its equation is $x^2 + y^2 + \alpha x + \beta y + \gamma = 0$,then find the value of $3(\alpha + \beta + \gamma)$.

If $P$ and $Q$ are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$,then for what value of $p$ does a circle pass through $P, Q$ and $(1, 1)$?

Consider the family of circles $x^2+y^2-2x-2\lambda y-8=0$. This family passes through two fixed points $A$ and $B$. Find the distance between these two points.