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

x^{2} + y^{2} = \frac{3}{2}

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x^{2} + y^{2} = 1

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x^{2} + y^{2} = \frac{27}{4}

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

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Solution

The correct option is D $x^{2} + y^{2} = \frac{9}{4}$
In $△ C P B,$

$cos \frac{π}{3} = \frac{C P}{C B} = \frac{\sqrt{h^{2} + k^{2}}}{3} \Rightarrow h^{2} + k^{2} = \frac{9}{4}$

$∴$ Required locus is $x^{2} + y^{2} = \frac{9}{4}$

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Let C be the circle with centre (0,0) and radius 3 units. The equation of the locus of the mid points of chord of the circle C that subtend an angle of 2π3 at its centre is

The correct option is D x2+y2=94In △CPB,cosπ3=CPCB=√h2+k23⇒h2+k2=94∴ Required locus is x2+y2=94

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

The correct option is D $x^{2} + y^{2} = \frac{9}{4}$
In $△ C P B,$

$cos \frac{π}{3} = \frac{C P}{C B} = \frac{\sqrt{h^{2} + k^{2}}}{3} \Rightarrow h^{2} + k^{2} = \frac{9}{4}$

$∴$ Required locus is $x^{2} + y^{2} = \frac{9}{4}$