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AP EAMCET201920 Apr 2019Morning ShiftMathematicsEllipseActual

(P ) is a variable point on the ellipse ( x^2 a^2 + y^2 b^2 =1 ) with foci (F₁ ) and (F₂ ). If (A ) is the area of the triangle (P F₁ F₂ ), then the maximum value of (A ) is

Options

  1. A( e a b )
  2. B( a e b )
  3. Caeb
  4. D( a b e )

Correct answer

C. aeb

Step-by-step solution

Let point (P(a , b ) ) on the ellipse ( x^2 a^2 + y^2 b^2 =1 ) ( ) Area of ( P F₁ F₂= 1 2 (2 a e) b| |=a e b| |=A ) For maximum value of (A, = 2 ) or ( 3 2 ) so (A_ =a e b ). Hence, option (c) correct.

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