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

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Solution

The correct option is B

Let $P (x_{1}, y_{1})$ be a point on the locus
$c o s \frac{π}{3} = \frac{O P}{O A} = \frac{\sqrt{x_{1}^{2} + y_{1}^{2}}}{3} = x_{1}^{2} + y_{1}^{2} = \frac{9}{4} ∴ E q u a t i o n t o t h e l o c u s i s x^{2} + y^{2} = \frac{9}{4}$

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

The correct option is B Let P(x1,y1) be a point on the locus cosπ3=OPOA=√x21+y213=x21+y21=94∴Equation to the 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 midpoints of the chords of the circle C that subtend an angle of $\frac{2 π}{3}$ at its centre is

The correct option is B

Let $P (x_{1}, y_{1})$ be a point on the locus
$c o s \frac{π}{3} = \frac{O P}{O A} = \frac{\sqrt{x_{1}^{2} + y_{1}^{2}}}{3} = x_{1}^{2} + y_{1}^{2} = \frac{9}{4} ∴ E q u a t i o n t o t h e l o c u s i s x^{2} + y^{2} = \frac{9}{4}$