2004 AMC 12B 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 \qquad\mathrm{(B)}\ \sqrt{10} \qquad\mathrm{(C)}\ \frac 72 \qquad\mathrm{(D)}\ \frac 92 \qquad\mathrm{(E)}\ 2\sqrt{14}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.