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JEE Main202226 Jun 2022Evening ShiftMathematicsEllipseActual

The locus of the mid-point of the line segment joining the point 4 , 3 and the points on the ellipse x 2 + 2 y 2 = 4 is an ellipse with eccentricity

Options

  1. A3 2
  2. B1 2 2
  3. C1 2
  4. D1 2

Correct answer

C. 1 2

Step-by-step solution

Given, x 2 4 + y 2 2 = 1 Let coordinate of D 2 cos θ + 4 2 , 2 sin θ + 3 2 ≡ h , k So, 2 h - 4 2 = cos θ             . . . 1 And 2 k - 3 2 = sin θ             . . . 2 Equation  1 2 + equation  2 2 , then we get 2 h - 4 2 2 + 2 k - 3 2 2 = 1 ⇒ x - 2 2 1 + y - 3 2 2 1 2 = 1 ∴   Required eccentricity is e = 1 - 1 2 = 1 2

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