If $P(2,3)$ and $Q(-1,2)$ are conjugate points with respect to the circle $x^2+y^2+2gx+3y-2=0$,then the radius of the circle is

$A$ line $y=mx+1$ intersects the circle $(x-3)^2+(y+2)^2=25$ at the points $P$ and $Q$. If the midpoint of the line segment $PQ$ has $x$-coordinate $-\frac{3}{5}$,then which one of the following options is correct?

If a straight line through $C(-\sqrt{8}, \sqrt{8})$ making an angle of $135^\circ$ with the $x$-axis cuts the circle $x = 5\cos\theta, y = 5\sin\theta$ at points $A$ and $B$,then the length of $AB$ is

$A$ circle $S$ touches the $Y$-axis at $(0,3)$ and makes an intercept of length $8$ units on the $X$-axis. If the centre $C$ of the circle $S$ lies in the second quadrant,then the distance of $C$ from the point $(-2,-1)$ is

The tangents drawn from a point $(2,-1)$ touch the circle $x^2+y^2+4x-2y+1=0$ at the points $A$ and $B$. If $C$ is the centre of the circle,then the area (in sq. units) of the triangle $ABC$ is

The length of the chord intercepted by the circle $x^2+y^2+2x+4y-20=0$ on the line $3x+4y-6=0$ is