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 -

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

Let $P (x_{1}, y_{1})$ be a point on the locus
$c o s \frac{π}{3} = \frac{O P}{O A} = \frac{\sqrt{x_{1}^{2} + y_{1}^{2}}}{3} = x_{1}^{2} + y_{1}^{2} = \frac{9}{4} ∴$ Equation to the locus is $x^{2} + y^{2} = \frac{9}{4}$

Suggest Corrections

Similar questions

Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. Locus of the point $P$ from which the chord of contact subtends an angle of $60^{\circ}$ at any point on the circumference of $C$ is

Q. 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 -

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 angles of

\frac{2 π}{3}

at its centre, is:

Q. The locus of the midpoints of chords of the circle

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

which subtends a right angle at the origin is

Q. The locus of midpoint of chord of the circle

x^{2} + y^{2} - 2 x - 2 y - 2 = 0

, which makes an angle of

120^{\circ}

at the centre, is

Join BYJU'S Learning Program

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
$c o s \frac{π}{3} = \frac{O P}{O A} = \frac{\sqrt{x_{1}^{2} + y_{1}^{2}}}{3} = x_{1}^{2} + y_{1}^{2} = \frac{9}{4} ∴$ Equation to the locus is $x^{2} + y^{2} = \frac{9}{4}$