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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+y22x2y3=0
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B
x2+y2+2x2y3=0
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C
x2+y2+2x+2y3=0
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D
none of these
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Solution

The correct option is A x2+y22x2y3=0
Given centroid of an equilateral triangle is G(1,1).
We know that in an equilateral triangle, centroid, circumcenter and incenter are at the same point.
So, the circumcenter is at G(1,1).
Given one vertex of equilateral triangle at A(1,2)
So, circumradius =AG=5
So, equation of circumcircle is
(x1)2+(y1)2=5
x2+y22x2y3=0

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