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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Circle

JEE Main 2005 · Mathematics · Circle

If the pair of lines a x^2+2(a+b) x y+b y^2=0 lie along diameters...

If the pair of lines ax2+2(a+b)xy+by2=0a 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. A3a2−10ab+3b2=03 a^2-10 a b+3 b^2=0
  2. B3a2−2ab+3b2=03 a^2-2 a b+3 b^2=0
  3. C3a2+10ab+3b2=03 a^2+10 a b+3 b^2=0
  4. D3a2+2ab+3b2=03 a^2+2 a b+3 b^2=0

Correct answer

D. 3a2+2ab+3b2=03 a^2+2 a b+3 b^2=0

Step-by-step solution

∣2(a+b)2−aba+b∣=1⇒(a+b)2=4(a2+b2+ab)⇒3a2+3b2+2ab=0.\begin{aligned}& \left|\frac{2 \sqrt{(a+b)^2-a b}}{a+b}\right|=1 \\ & \Rightarrow(a+b)^2=4 \left(a^2+b²+a b\right) \\ & \Rightarrow 3 a²+3 b²+2 a b=0 . \end{aligned} $
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