First slide

Definition of a circle

Question

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

Moderate

A

$x^{2} + y^{2} - 4 x + 4 y - 10 = 0$
B

$x^{2} + y^{2} + 4 x - 4 y + 10 =$
C

$x^{2} + y^{2} + 4 x - 4 y - 10 = 0$
D

$x^{2} + y^{2} - 4 x + 4 y + 10 =$

Solution

Circumcircle of the equilateral triangle has
centre at(2, - 2) and passes through(-1, 1). So, its equation is
$\begin{array}{l} (x - 2)^{2} + (y + 2)^{2} = (2 + 1)^{2} + (- 2 - 1)^{2} \\ \Rightarrow x^{2} + y^{2} - 4 x + 4 y - 10 = 0 \end{array}$

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