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Q.

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 2π3 at its center is

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a

x2+y2=32

b

x2+y2=1

c

x2+y2=274

d

x2+y2=94

answer is D.

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Detailed Solution

Let M(h,k) be the mid-point  of chord AB where ∠ACB=2π3∴∠ACM=π3 Also CM=3cosπ3=32⇒h2+k2=32⇒h2+k2=94∴ Locus of (h,k) is x2+y2=94
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