The circle passing through $\left(t,1\right),\left(1,t\right)$ and $\left(t,t\right)$ for all values of $t$ also passes through ;

The image of the circle $(x - 3)^2 + (y - 2)^2 = 1$ in the line mirror $ax + by = 19$ is $(x - 1)^2 + (y - 16)^2 = 1$ then values of (a, b) is

The centre of a circle is $(2a, a-7$). Find the values of $a$ if the circle passes through the point (11, -9) and has diameter $10\sqrt{2}$ units.

The centres of a set of circles, each of radius $3$, lie on the circle ${x}^{2}+{y}^{2}=25$. The lotus of any point in the set is ;