If the equation of the circle whose radius is $3$ units and which touches internally the circle $x^2+y^2-4x-6y-12=0$ at the point $(-1,-1)$ is $x^2+y^2+px+qy+r=0$,then $p+q-r=$

Consider $L_1: 2x + 3y + p - 3 = 0$; $L_2: 2x + 3y + p + 3 = 0$,where $p$ is a real number,and $C: x^2 + y^2 + 6x - 10y + 30 = 0$.
$STATEMENT-1$: If line $L_1$ is a chord of circle $C$,then line $L_2$ is not always a diameter of circle $C$.
$STATEMENT-2$: If line $L_1$ is a diameter of circle $C$,then line $L_2$ is not a chord of circle $C$.

If a circle $C_1: x^2+y^2=16$ intersects another circle $C_2$ with radius $5$ such that the common chord is of maximum length and has a slope equal to $\frac{3}{4}$,then the centre of the circle $C_2$ is

If two distinct chords,drawn from the point $(p, q)$ on the circle ${x^2} + {y^2} = px + qy$ (where $pq \neq 0$),are bisected by the $x$-axis,then:

If the circle $x^2 + y^2 = a^2$ cuts a chord of length $2b$ on the line $y = mx + c$,then:

$S_1$ and $S_2$ are two concentric circles of radii $1$ and $2$ respectively. Two parallel tangents to $S_1$ cut off an arc from $S_2$. The length of the arc is