Again an Ellipse Problem !!!!!!

A tangent to the ellipse $\frac { { x }^{ 2 } }{ { 4 }^{ 2 } } +\frac { { y }^{ 2 } }{ { 3 }^{ 2 } }$ cuts the coordinate axes in A and B. Then the equation of the locus of the middle point of AB is:-

=> The equation is of the form $\frac { { a }^{ b } }{ x^{ 2 } } +\frac { { c }^{ d } }{ y^{ 2 } } =e$ where a,b,c,d,e are positive integers which are not necessarily different then find a+b+c+d+e.