If the coordinates of one end of the diameter of the circle $x^2 + y^2 - 8x - 4y + c = 0$ are $(-3, 2)$,then the coordinates of the other end are:

$x^2+y^2+2x-6y-6=0$ and $x^2+y^2-6x-2y+k=0$ are two intersecting circles and $k$ is not an integer. If $\theta$ is the angle between the two circles and $\cos \theta = \frac{-5}{24}$,then $k=$

If the point $(\lambda, 1+\lambda)$ lies inside the circle $x^2+y^2=1$,then

$A$ cow is tied to a post by a rope. The cow moves along a circular path,always keeping the rope tight. If it describes an arc of $44 \ m$ when it has traced out $72^{\circ}$ at the centre,the length of the rope is: (in $m$)

Let a triangle $ABC$ be inscribed in the circle $x^{2} - \sqrt{2}(x+y) + y^{2} = 0$ such that $\angle BAC = \frac{\pi}{2}$. If the length of side $AB$ is $\sqrt{2}$,then the area of the $\triangle ABC$ is equal to

The two circles $x^2 + y^2 - 4y = 0$ and $x^2 + y^2 - 8y = 0$: