JEE Main 2024 Mathematics question
Let P be a parabola with vertex (2, 3) and directrix 2x + y = 6. Let an ellipse E : x²/a² + y²/b² = 1, a > b, of eccentricity 1/√2 pass through the focus of the parabola P. Then, the square of the length of the latus rectum of E, is
Answer: (D)
Solution
The foot of the perpendicular from the vertex (2, 3) to the directrix is z = (8/5, 14/5). The vertex is the midpoint of z and the focus F, so F = (12/5, 16/5). The
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