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Let P(3cosα, 2sinα), α ≠ 0, be a point on the ellipse x^2 9+ y^2 4=1, Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line…

JEE Main 2026 — Mathematics Coordinate Geometry

2026mcqmedium

Let P(3cos⁡α,2sin⁡α)P(3\cos\alpha, 2\sin\alpha)P(3cosα,2sinα), α≠0\alpha \neq 0α=0, be a point on the ellipse x29+y24=1\dfrac{x^2}{9}+\dfrac{y^2}{4}=19x2​+4y2​=1, QQQ be a point on the circle x2+y2−14x−14y+82=0x^2+y^2-14x-14y+82=0x2+y2−14x−14y+82=0 and RRR be a point on the line x+y=5x+y=5x+y=5 such that the centroid of the triangle PQRPQRPQR is (2+cos⁡α,3+23sin⁡α)\left(2+\cos\alpha, 3+\dfrac{2}{3}\sin\alpha\right)(2+cosα,3+32​sinα). Then the sum of the ordinates of all possible points RRR is:

Official previous-year question

Held on 4 Apr 2026 · Verified 6 Jul 2026.

Options

  1. A

    666

  2. B

    222

  3. C

    444

  4. D

    888

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