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
(a) x² + y² − 2x − 2y − 3 = 0
(b) x² + y² + 2x − 2y − 3 = 0
(c) x² + y² + 2x + 2y − 3 = 0
(d) none of these

Answer 1

(a) 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:
${\left(x-1\right)}^2+{\left(y-1\right)}^2=5$
$\Rightarrow x^2+y^2-2x-2y-3=0$