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KVPY2012MathematicsEllipse

Consider the conic ex ²+ y²-2 e ² x -2 ² y + e ³+ ³= e . Suppose P is any point on the conic and S ₁, ~S ₂ are the foci of the conic, then the maximum value of ( PS ₁+ PS ₂ ) is -

Options

  1. Ae
  2. Be
  3. C2
  4. D2 e

Correct answer

C. 2

Step-by-step solution

e x²+ y²-2 e² x-2 ² y+e³+ ³= ee (x²-2 e x+e² )+ (y²-2 y+ ² )= e (x-e)² + (y- )² e =1a²= a= >eP S₁+P S₂=2 a Major axis is | to axis P S₁+P S₂=2 F

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