Find equation of line passing through $(20,12)$ such that the area of the triangle formed by the line and the positive axis is smallest possible.
Also: $\frac{x}{a}+\frac{x}{b}=1$
where $a, b$ are x, y intercepts
So far, I have
$A=\frac{1}{2}ab, \qquad line = (20,12)+\lambda(a,-b)$
I need to find min area, so I need to differentiate $A$ but with respect to what? From what I have, I can't really find a way to express 1 term in terms of another. If I try to express 1 term in terms of 3 others from $\frac{x}{a}+\frac{x}{b}=1$, it doesn't appear useful.
UPDATE
I think the picture will look like: