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JEE Main202225 Jul 2022Evening ShiftMathematicsEllipseActual

If the ellipse x 2 a 2 + y 2 b 2 = 1 meets the line x 7 + y 2 6 = 1 on the x -axis and the line x 7 - y 2 6 = 1 on the y -axis, then the eccentricity of the ellipse is

Options

  1. A5 7
  2. B2 6 7
  3. C3 7
  4. D2 5 7

Correct answer

A. 5 7

Step-by-step solution

Given, x 2 a 2 + y 2 b 2 = 1 meets the line x 7 + y 2 6 = 1 on the x -axis, so at x - axis y = 0 putting in both equation and comparing we get, a = 7 And x 2 a 2 + y 2 b 2 = 1 meets the line x 7 - y 2 6 = 1 on the y -axis where x = 0 so putting in both equation and comparing we get, b = 2 6 Therefore, e 2 = 1 - b 2 a 2 = 1 - 24 49 ⇒ e = 25 49 = 5 7

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