A circle has equation \(x^{2}+y^{2}-25=0\).
A second circle has the same radius as the first circle, and the coordinates of its centre are both positive.
The two circles intersect at the points \(A\) and \(B\).
The line \(A B\) has length 6 and is parallel to the line \(y=-x\).
Find the equation of the second circle in the form \(x^{2}+y^{2}+a x+b y+c=0\), where \(a, b\) and \(c\) are constants.