JEE Main 2024 Mathematics question
Let P be a point on the ellipse . Let the line passing through P and parallel to y-axis meet the circle x² + y² = 9 at point Q such that P and Q are on the same side of the x-axis. Then, the eccentricity of the locus of the point R on PQ such that PR : RQ = 4 : 3 as P moves on the ellipse, is:
Answer: (B)
Solution
P = (3cosθ, 2sinθ), Q = (3cosθ, 3sinθ); R = (3cosθ, (2 + 4/7)sinθ) = (3cosθ, (18/7)sinθ), an ellipse
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