In an ellipse, what is the relation between semi-major axis a, semi-minor axis b, and eccentricity e?
Answer and explanation
Correct answer: C. b^2 = a^2 (1 - e^2)
- Step 1: For an ellipse with a > b, eccentricity e = sqrt(1 - b^2/a^2). Step 2. Squaring both sides: e^2 = 1 - b^2/a^2 => b^2/a^2 = 1 - e^2 => b^2 = a^2 (1 - e^2). Answer: b^2 = a^2 (1 - e^2). Why not the others: a^2 = b^2 (1 - e^2) swaps a and b; b^2 = a^2 (1 + e^2) applies to hyperbolas; e^2 = 1 + b^2/a^2 is for hyperbolas.
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