The intercept on the line $y=x$ by the circle $x^2+y^2-2x=0$ is $AB$. The equation of the circle with $AB$ as diameter is:

Let $P$ and $Q$ be two distinct points on a circle which has center at $C(2,3)$ and which passes through the origin $O(0,0)$. If $OC$ is perpendicular to both the line segments $CP$ and $CQ$,then the set $\{P, Q\}$ is equal to:

If the two circles $(x-1)^2+(y-3)^2=r^2$ and $x^2+y^2-8x+2y+8=0$ intersect at two distinct points,then

Let $\theta$ be the angle between the circles $S \equiv x^2+y^2+2x-2y+c=0$ and $S' \equiv x^2+y^2-6x-8y+9=0$. If $c$ is an integer and $\cos \theta = \frac{5}{16}$,then the radius of the circle $S=0$ is

The area of a circle having the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as two of its tangents is:

The number of integral values of $k$ for which the line $3x + 4y = k$ intersects the circle $x^{2} + y^{2} - 2x - 4y + 4 = 0$ at two distinct points is