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MCQMediumJEE Main 2026 · 21 January, Shift 2Conic Sections (Parabola, Ellipse, Hyperbola)

Mathematics Question from JEE Main 2026 · 21 January, Shift 2

If the line ax+4y=7ax + 4y = \sqrt{7}, where a∈Ra \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 :

  • A

    13+125\frac{1}{\sqrt{3}} + \frac{1}{2\sqrt{5}}

  • B

    13+127\frac{1}{\sqrt{3}} + \frac{1}{2\sqrt{7}}

  • C

    13−125\frac{1}{\sqrt{3}} - \frac{1}{2\sqrt{5}}

  • D

    13−1211\frac{1}{\sqrt{3}} - \frac{1}{2\sqrt{11}}

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