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MathsJEE Main 6 Apr 2026, Shift 2·Q12·MCQ·Moderate

Conic Sections · Locus of chord midpoint ellipse

Let x=9x = 9 be a directrix of an ellipse EE, whose centre is at the origin and eccentricity is 13\dfrac13. Let P(α,0)P(\alpha, 0), α>0\alpha > 0, be a focus of EE and ABAB be a chord passing through PP. Then the locus of the mid point of ABAB is:
  1. (1)9y2=8x(1−x)9y^2 = 8x(1 - x)
  2. (2)3y2=4x(1−x)3y^2 = 4x(1 - x)
  3. (3)9y2=8x(x−1)9y^2 = 8x(x - 1)
  4. (4)3y2=4x(x−1)3y^2 = 4x(x - 1)

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