# Call for coordinate?

Calculus Level 3

A curve passing through the point $$(1,1)$$ has the property that the perpendicular distance of the origin from the normal at any point $$P$$ of the curve is equal to the distance of $$P$$ from the $$x$$-axis .

Let the equation of the curve be of the form

$ax^2 +by^2 + 2hxy +2gx+2fy+c = 0$

for integers $$a,b,c,g,h$$ and $$f$$. where $$a,b$$ are coprime positive integers

Calculate $$a+b+2g$$.

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