question_answer

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

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)  \[{{x}^{2}}+{{y}^{2}}={{d}^{2}}\]

Correct Answer: C

Solution :

In an equilateral triangle, the circumcentre of a circle lies on the centroid of the triangle. Here, radius of circles is 2a. \[\therefore \]    Required equation of circle is \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]