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

$x^{2} + y^{2} - 2 x - 2 y - 3 = 0$

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$x^{2} + y^{2} + 2 x - 2 y - 3 = 0$

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$x^{2} + y^{2} + 2 x + 2 y - 3 = 0$

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none of these

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Solution

The correct option is A
$x^{2} + y^{2} - 2 x - 2 y - 3 = 0$

$x^{2} + y^{2} - 2 x - 2 y - 3 = 0$
Fig.

The centre of the circumcircle is (1, 1).

Radius of the circumcircle

$= \sqrt{(1 + 1)^{2} + (1 - 2)^{2}} = \sqrt{5}$

$∴$ Equation of the circle :

$(x - 1)^{2} + (y - 2)^{2} = 5$

$\Rightarrow x^{2} + y^{2} - 2 x - 2 y - 3 = 0$

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