Two rods of length \(7\) and \(14\) slide along the coordinate axes in a manner that their end are always concyclic as shown in figure. Find the locus of center of the circle passing through these ends. Equation will be of form: \[a x^c +b y^d + e =0\] Find \(a+b+c+d+e\).
The rod of length 7 slides on the y-axis, the rod of length 14 slides on the x-axis.
\(a,b, c, d, e \) are integers.
\(a \) is positive.
\(a \) and \(e \) are coprime.