AMC 12 2004b Problem 21

The graph of $2x^2 + xy + 3y^2 - 11x - 20y + 40 = 0$ is an ellipse in the first quadrant of the $xy$-plane. Let $a$ and $b$ be the maximum and minimum values of $\frac yx$ over all points $(x,y)$ on the ellipse. What is the value of $a+b$?

$\mathrm{(A)}\ 3 \mathrm{(B)}\ \sqrt{10} \mathrm{(C)}\ \frac 72 \mathrm{(D)}\ \frac 92 \mathrm{(E)}\ 2\sqrt{14}$