Question

If the centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is

Options

• x² + y² − 2x − 2y − 3 = 0

• x² + y² + 2x − 2y − 3 = 0

• x² + y² + 2x + 2y − 3 = 0

• none of these

Answer 1

 x² + y² − 2x − 2y − 3 = 0

The centre of the circumcircle is (1, 1).
Radius of the circumcircle = \[\sqrt{\left( 1 + 1 \right)^2 + \left( 1 - 2 \right)^2} = \sqrt{5}\]

∴ Equation of the circle: \[\left( x - 1 \right)^2 + \left( y - 1 \right)^2 = 5\]

\[\Rightarrow x^2 + y^2 - 2x - 2y - 3 = 0\]