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JEE Main 2019 · 12 April · Shift II

JEE Main 2019 Mathematics question on Conic Sections

An ellipse, with foci at (0,2)(0, 2) and (0,−2)(0, -2) and minor axis of length 4, passes through which of the following points?
  1. A.
    (2,2)(\sqrt{2}, 2)
  2. B.
    (2,2)(2, \sqrt{2})
  3. C.
    (2,22)(2, 2\sqrt{2})
  4. D.
    (1,22)(1, 2\sqrt{2})
Show answer and solution

Correct option: A

Solution

The foci are on the y-axis, so the ellipse is x²/b² + y²/a² = 1 with a > b. The distance between foci is 2c = 4, so c = 2. The minor axis has length 2b = 4, so b = 2. Then a² = b² + c² = 4 + 4 = 8. The equation is x²/4 + y²/8 = 1. Plugging in (√2, 2): (2/4) + (4/8) = 1/2 + 1/2 = 1. ✓

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