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Question

If F1 and F2 are the feet of the perpendiculars from the foci S1 & S2 of an ellipse fraction numerator x to the power of 2 end exponent over denominator 5 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 3 end fraction equals 1 on the tangent at any point P on the ellipse, then (S1 F1). (S2 F2) is equal to-

  1. 2    
  2. 3    
  3. 4    
  4. 5    

hintHint:

find out the values of a,b and e from the equation. assume a point on the ellipse and find out the values of required distances.

The correct answer is: 3


    3
    a= √5
    b= √3
    e= √(1-3/5) = √(2/5)
    let’s assume the point p to be at the end of the major axis.
    in this case,
    S1F1 = a-ae
    S2F2= a+ae
    (a-ae)(a+ae) = a2-a2e2 = 5-5(2/5)
    3

    selecting a point on the major axis provides an ease of calculation.

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