First slide

Definition of a circle

Question

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3 a is

Moderate

A

$x^{2} + y^{2} = 9 a^{2}$
B

$x^{2} + y^{2} = 16 a^{2}$
C

$x^{2} + y^{2} = 4 a^{2}$
D

$x^{2} + y^{2} = a^{2}$

Solution

It is given that the triangle is equilateral. Therefore, centroid of the triangle is same as the circumcircle.
Also, Radius of the circumcircle $= \frac{2}{3}$ (median) $= \frac{2}{3} (3 a) = 2 a$
Hence, the equation of the circumcircle whose centre is at
(0, 0) and radius $2 a,$ is $x^{2} + y^{2} = (2 a)^{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App