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JEE Main20253 Apr 2025Evening ShiftMathematicsEllipseActual

Let C be the circle of minimum area enclosing the ellipse E: x^2 a^2 + y^2 b^2 =1 with eccentricity 1 2 and foci ( 2,0) . Let PQR be a variable triangle, whose vertex P is on the circle C and the side Q R of length 29 is parallel to the major axis of E and contains the point of intersection of E with the negative y -axis. Then the maximum area of the triangle PQR is :

Options

  1. A6(3+ 2 )
  2. B8(3+ 2 )
  3. C62+ 3
  4. D82+ 3

Correct answer

D. 82+ 3

Step-by-step solution

Area of P Q R aligned & = 1 2 (2 a)(a +b) & maximum area =a(a+b) & =4(4+2 3 )=8(2+ 3 ) aligned

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