# JEEometry :3

Geometry Level 5

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.

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