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MathsJEE Main 21 Jan 2026, Shift 2·Q4·MCQ·Moderate

Conic Sections · Ellipse tangent and focal distance

If the line αx+4y=7\alpha x + 4y = \sqrt7, where α∈R\alpha \in \mathbb{R}, touches the ellipse 3x2+4y2=13x^2 + 4y^2 = 1 at the point PP in the first quadrant, then one of the focal distances of PP is:
  1. (1)13−1211\dfrac{1}{\sqrt3} - \dfrac{1}{2\sqrt{11}}
  2. (2)13+125\dfrac{1}{\sqrt3} + \dfrac{1}{2\sqrt5}
  3. (3)13−125\dfrac{1}{\sqrt3} - \dfrac{1}{2\sqrt5}
  4. (4)13+127\dfrac{1}{\sqrt3} + \dfrac{1}{2\sqrt7}
We corrected a printing error in the original paper

Source printed “In the line” for “If the line”.

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