Approach: So we know the ellipse is just the scaled shadow of a circle.Let’s find the scaling factor.
x^2/a^2 + y^2/b^2 = 1 is an ellipse. Rewrite this as: (y*(a/b))^2+x^2 = a^2
This is just a vertically scaled down circle of radius a (think light falls from the top at an angle), and the vertical factor is a/b. The biggest triangle in the ellipse is then a scaled up version of the biggest triangle in the circle. Using a little geometry and taking symmetry into account, we can understand that the biggest such triangle is the equilateral one. It’s sides will be √3a and the area will be (3√3)a^2/4 Translating this to ellipse terms – we scale the horizontal dimension up by a factor a/b, and the area of the biggest triangle in the ellipse is,
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