The length of the chord of the circle $x^{2}+y^{2}+3x+2y-8=0$ intercepted by the $y$-axis is

The length of the diameter of a circle which touches the $x$-axis at the point $(1, 0)$ and passes through the point $(2, -3)$ is:

Let $A(2, 3)$,$B(4, 5)$ and let $C = (x, y)$ be a point such that $(x - 2)(x - 4) + (y - 3)(y - 5) = 0$. If the area of $\Delta ABC = \sqrt{2} \text{ sq. unit}$,then the maximum number of positions of $C$ in the $xy$ plane is:

If one end of the diameter of the circle $x^2+y^2-4x-6y+11=0$ is $(3,4)$,then the other end of the diameter is

The least distance of the point $(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is

$ABC$ is a triangle and the radical centre of the circles with $AB, BC, CA$ as the diameters is $(-6,5)$. If $A=(3,2)$ and $B=(2,1)$,then $C=$