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A set of lines x+y-2+ ₁(2 x+y-3)=0 represents incident rays on an ellipse S=0 and 2 x+3 y-23+ ₂(2 x-y-3)=0 represents the set of reflective rays from the ellipse where ₁, ₂ R . If P (3,7) is a point on the ellipse normal at which meets the major axis at N .

Options

  1. AEccentricity of ellipse is 5 2 2 +1
  2. BN divides line segment joining two foci in the ratio 2 2 : 1
  3. CArea of triangle formed by point P and two foci 5
  4. DEccentricity of ellipse is 5 2 2 -1

Correct answer

C. Area of triangle formed by point P and two foci 5

Step-by-step solution

2 ae =5,2 a =(2 2+1) 5, e 5 2 2 +1 Foci are S ₁(1,1) and S ₂(4,5) S ₁ ~N ~S ₂ ~N = PS ₁ PS ₂ = 40 5 =2 2

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