JEE Main 2026 Mathematics question
Consider the parabola P : y² = 4kx and the ellipse E : . Let the line segment joining the points of intersection of P and E, be their latus rectums. If the eccentricity of E is e, then e² + 2√2 is equal to .
Answer: 3
Solution
Matching the latus rectums gives k = ae and 2k = b²/a, leading to e² + 2e − 1 = 0, so e = √2 − 1. Then e² = 3 − 2√2, and e² + 2√2 = 3.