Question

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 $\frac{2\pi }{3}$ at its centre is -

• A. $x^2+y^2=\frac{27}{4}$
• B. $x^2+y^2=\frac{9}{4}$
• C. $x^2+y^2=\frac{3}{2}$
• D. $x^2+y^2=1$

Answer 1

The correct option is B $x^2+y^2=\frac{9}{4}$


Let $P(x_1,y_1)$ be a point on the locus
$cos\frac{\pi }{3}=\frac{OP}{OA}=\frac{\sqrt{x_1^2+y_1^2}}{3}=x_1^2+y_1^2=\frac{9}{4}\therefore$ Equation to the locus is $x^2+y^2=\frac{9}{4}$