QJEEM06Macf62: JEE Main 2006 Mathematics - Class 11 JEEM06Macf62 Solution: Let C be the circle with centre ( 0 , 0 ) and radius 3 units.…

Question

Verified Solution • 2025–26 Session moderate

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 π}{3}

at its center is :

Accepted Answer

Let

M (h, k)

be the mid point of chord

A B

where

∠ A O B = \frac{2 π}{3}

∴

∠ A O M = \frac{π}{3} .

Also

O M =

3 \cos \frac{π}{3} = \frac{3}{2}

\Rightarrow \sqrt{h^{2} + k^{2}} = \frac{3}{2}

\Rightarrow h^{2} + k^{2} = \frac{9}{4}

∴

Locus of

(h, k)

is

x^{2} + y^{2} = \frac{9}{4}

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