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

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 image of the centre of the circle $$x^2+y^2=a^2$$ with respect to the mirror $$x+y=1$$ 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