The locus of the mid-point of a chord of the circle $x^2+y^2-2x-2y-23=0$ of length $8$ units is

The values of $\text{'}a\text{'}$ for which the common chord of the circles $x^2+y^2=8$ and ${\left(x-a\right)}^2+y^2=8$ subtends a right angle at the origin are

The locus of the centre of the circles passing through $\left(1,1\right)$ and cutting $x^2+y^2=4$ orthogonally is

Tangents are drawn to the circle $x^2+y^2=9$ at the points where it is met by the circle $x^2+y^2+3x+4y+2=0$. The point of intersection of these tangents will be