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Find the coordinates of the centre of the circle \(3x^{2}+3y...

Find the coordinates of the centre of the circle 3x2+3y24x+8y2=0

A.

(-2,4)

B.

(23,43)

C.

(23,43)

D.

(2, -4)

Correct answer is C

The equation for a circle with centre coordinates (a, b) and radius r is

(xa)2+(yb)2=r2

Expanding the above equation, we have

x22ax+a2+y22by+b2r2=0 so that

x22ax+y22by=r2a2b2

Taking the original equation given, 3x2+3y24x+8y=2 and making the coefficients of x2 and y2 = 1,

x2+y24x3+8y3=23, comparing, we have

2a=43;2b=83

a=23;b=43