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JEE Main2005MathematicsCircleActual

If the pair of lines a x^2+2(a+b) x y+b y^2=0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

Options

  1. A3 a^2-10 a b+3 b^2=0
  2. B3 a^2-2 a b+3 b^2=0
  3. C3 a^2+10 a b+3 b^2=0
  4. D3 a^2+2 a b+3 b^2=0

Correct answer

D. 3 a^2+2 a b+3 b^2=0

Step-by-step solution

aligned & | 2 (a+b)^2-a b a+b |=1 & (a+b)^2=4 (a^2+b^2+a b ) & 3 a^2+3 b^2+2 a b=0 . aligned

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