Q88 / 150 · JEE Main 2006 · Mathematics

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

  • A
    $x^2+y^2=\frac{3}{-}$
  • B
    $x^2+y^2=1$
  • C
    $x^2+y^2=\frac{27}{4}$
  • Correct answer
    D
    $x^2+y^2=\frac{9}{4}$

Solution

$\cos \frac{\pi}{3}=\frac{\sqrt{h^2+k^2}}{3} \Rightarrow h^2+k^2=\frac{9}{4}$

Hence, the correct answer is option: 'D'.

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