Question

Origin is the centre of circle passing through the vertices of an equilateral triangle whose median is of length $3a$ then equation of the circle is?

• A. $x^2+y^2=a^2$
• B. $x^2+y^2=2a^2$
• C. $x^2+y^2=3a^2$
• D. $x^2+y^2+4a^2$

Answer 1

The correct option is D $x^2+y^2+4a^2$

Equation of a circle passing through the origin is $x^2+y^2=a^2$

If the centroid of the triangle with the centre of the circle, then the radius of the circle is $\frac{2}{3}$ of the length of the medion.

$\therefore r=\frac{2}{3}\times 3a$

$⟶r^2=4a^2$

$\therefore x^2+y^2=4a^2$