The equation of the circle with radius 3 and centre as the point of intersection of the lines  $2x+3y=5,$ $2x-y=1$ is

Given lines are $2x+3y=5$…..(1), $2x-y=1$….(2)

Point of Intersection of (1)&(2)= $\left(1,1\right)=\left(h,k\right)$$r=3$

Equation of circle is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

$\Rightarrow {\left(x-1\right)}^2+{\left(y-1\right)}^2=9$

$\Rightarrow x^2+y^2-2x-2y-7=0$