# 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 \(a+b+c+d+e+f+g\).