How do you derive the equation of an ellipse given its major and minor axes lengths as well as its foci coordinates, and prove that the distance sum of a point to its foci is constant?
Answer 1
Jeffrey Shannon
Given the lengths of the major axis (2a) and minor axis (2b), and the coordinates of the foci at (±c, 0), the standard form of the ellipse equation is (x²/a²) + (y²/b²) = 1. To prove the distance sum is constant, note that for any point (x, y) on the ellipse, the sum of distances to the foci (d1 + d2) equals 2a, which is constant.
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