The equation of a circle is given by ^{2}/_{3} x^{2} + ^{2}_{/3} y^{2} - 4x+ 2 ^{2}/_{3} y - 2 = 0. Determine the centre and the radius of the circle.

^{3}/_{2} x ( ^{2}/_{3}x^{2} + ^{2}/_{3}y^{2} - 4x + 2 ^{2}/_{3}y - 2=0)= x^{2} + y^{2} - 6x + 4y -3 = 0x^{2} - 6x + 9 + y^{2} + 4y + 4 = 3 + 9 + 4(x - 3)^{2} ( y +2)^{2} = 4^{2}centre = (3,-2)Radius = 4 units

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