# Looks easy but still Dangerous.

Calculus Level 5

A curve passing through the origin, is such that the middle point of the segment of normal between point of contact and $$x$$-axis lies on the parabola $$2y^2 = x$$, then the equation the curve is $$a_{1}y^{a_{2}} = a_{3}x + a_{4} - a_{5}e^{a_{6}x}$$. Find the value of $$a_{1} +a_{2} + a_{3} +a_{4} + a_{5} + a_{6}$$.

Given that $$a_{1},a_{2},a_{3},a_{4},a_{5},a_{6}$$ are integers which may or may not be equal with $$a_{1}$$ > 0 and their HCF is 1.

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