# A Troubling Problem!

Geometry Level 4

The locus of the foot of perpendicular drawn from the center of the ellipse $${ x }^{ 2 }+{ 3y }^{ 2 }=6$$ on any tangent to it is of the form $${ ({ x }^{ a }+{ y }^{ b }) }^{ c }=d{ x }^{ e }+f{ y }^{ g }$$ where $$a,b,c,d,e,f,g$$ are positive integers which are not necessarily different.

=> Then Find Value of $$a+b+c+d+e+f+g$$.

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