Circle

Let $c_1: x^2+y^2=1$ and $c_2:(x-10)^2+y^2=9$ be two circles a line touching $c_1$ at $P$ and $c_2$ at $Q$. If $M$ is the mid-point of $P Q$, then $M$ lies on a circle $(x-5)^2+y^2=r^2$ where ' $r$ ' is $(r>0)$

In the given figure, the equation of the large circle is $x^2+y^2+4 y-5=0$ and the distance between centre is 4 . Then, the equation of smaller circle is

If two different circles $x^2+y^2+2 a x+2 b y+1$ $=0$ and $x^2+y^2+2 b x+2 a y+1=0$ touches each other, then $(a+b)^2$ is equal to

If the tangent at the point $P$ on the circle $x^2+y^2+2 x+2 y=7$ meets the straight line $3 x-4 y=15$ at the point $Q$ on the $X$-axis, then length of $P Q$ is

The line \(a x+b y+c=0\) will be a tangent to the circle \(x^2+y^2=r^2\), then

The image of the centre of the circle \(x^2+y^2=a^2\) with respect to the mirror \(x+y=1\) is

If the tangent at point \(P\) on the circle \(x^2+y^2+6 x+6 y-2=0\) meets the straight line \(5 x-2 y+6=0\) at a point \(Q\) on \(Y\)-axis, the length of \(P Q\) is

If a circle of constant radius '\(r\)' passes through the origin and meets the coordinate axes at points \(A\) and \(B\) respectively, then the locus of the centroid of triangle \(O A B\), '\(O\)' being the origin, is

The radius of the circle \((x \cos \theta+y \sin \theta-a)^2+(x \sin \theta-y \cos \theta-b)^2=k^2\) is