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Graph of a Linear Function in Two Variables

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Two vertices of an equilateral triangle are (-1, 0)and (1, 0) and its third vertex lies above the x-axishe equation of circumcircle is(1) x2+y2 2y310 (2) x2+y2-y(3) x2+ y2 2y1-0 (4) x2+ y2 x y 03

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Q. 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

Q. Two vertices of an equilateral triangle are

(- 1, 0)

(1, 0)

and its third vertex lies above the

X

-axis. Find equation of its circumcircle.

Q. Two vertices of an equilateral triangle are (–1, 0) and (1, 0) and its third vertex lies above the x-axis, the equation of the circumcircle is

Q. The equation of the circumcircle of the triangle formed by the lines

y + \sqrt{3} x = 6, y - \sqrt{3} x = 6,

y = 0,

A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3})

are the vertices of an equilateral triangle and

(x_{1} - 4)^{2} + (y_{1} - 5)^{2} = (x_{2} - 4)^{2} + (y_{2} - 5)^{2} = (x_{3} - 4)^{2} + (y_{3} - 5)^{2},

then the value of

(y_{1} + y_{2} + y_{3}) - (x_{1} + x_{2} + x_{3})

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