Let C be the circle with centre 0 ,   0 and radius 3   unit . The equation of the locus of the mid…

Let C be the circle with centre 0, 0 and radius 3 unit. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of 2π3 at its centre, is:
  1. x2+y2=1
  2. x2+y2=274
  3. x2+y2=94
  4. x2+y2=32

Solution

Let the coordinates of a point P be (h, k) which is mid point of the chord AB.

Now, OP=h-02+k-02

=h2+k2

In ∆AOP, cos⁡π3=OPOA


⇒  12=h2+k23

⇒   h2+k2=94

Hence, the required locus is

x2+y2=94.

Asked in: AP EAMCET 2021 (20 Aug Shift 1)

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