You mean "passing through the points of intersection".

Geometrically speaking,

you are looking for a point on the line x=2 that is equidistant from the two points of intersection of the circles, so that both points are a radius away.

Solve for the points of intersection of the circles.

Then use Pythagoras' theorem to find the y co-ordinate of the new circle centre.

Then find that circle's radius.

You can then write the circle equation.