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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Mathematics
Chapter
Circle

JEE Main 2006 · Mathematics · Circle

Let C be the circle with centre (0,0) and radius 3 units. The...

Let CC be the circle with centre (0,0)(0,0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle CC that subtend an angle of 2π3\frac{2 \pi}{3} at its centre is

Options

  1. Ax2+y2=3−x^2+y^2=\frac{3}{-}
  2. Bx2+y2=1x^2+y^2=1
  3. Cx2+y2=274x^2+y^2=\frac{27}{4}
  4. Dx2+y2=94x^2+y^2=\frac{9}{4}

Correct answer

D. x2+y2=94x^2+y^2=\frac{9}{4}

Step-by-step solution

cos⁡π3=h2+k23⇒h2+k2=94\cos \frac{\pi}{3}=\frac{\sqrt{h^2+k^2}}{3} \Rightarrow h^2+k^2=\frac{9}{4}
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