Ellipse In A Box

Find the relationship between "B" and "D" that guarantees that this conic section:

x² + Bxy + 4y² = D will be an ellipse, trapped in the box with vertices at:

(-2, 1), (2, 1), (2, -1) and (-2, -1).

Find "D" as a function of "B."

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Hint: You'll need to take the derivative and look at how you can keep the vertical tangents on the left and right sides of the box, and the horizontal tangents on the top and bottom of the box.

What are the restrictions on the domain of "B" that keep it inside the box (and an ellipse, rather than an hyperbola, or a straight line).

Dave Matthews, Created with GeoGebra