# No Integration Necessary

Geometry Level 4

The figure above shows the graph of an ellipse having a horizontal semi-major axis of 2 units, and a vertical semi-minor axis of 1 unit. That is, its equation is

$\frac{x^2}{4} + y^2 = 1$

Two perpendicular lines (shown in red) are at 45 degrees with the $$x$$-axis, and pass through the origin. They segment the ellipse into 4 segments. From symmetry, there are only two distinct values of the area of a segment. Find the ratio of the area of the larger segment to the area of the smaller segment.

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