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The equation of a circle is \(3x^{2} + 3y^{2} + 24x - 12y = ...

The equation of a circle is 3x2+3y2+24x12y=15. Find its radius.

A.

2

B.

3

C.

4

D.

5

Correct answer is D

The equation of a circle is given as: (xa)2+(yb)2=r2

Expanding, we have: x2+y22ax2by+a2+b2=r2

x2+y22ax2by=r2a2b2

Comparing with the given equation: 3x2+3y2+24x12y=15

Making the coefficients of x2 and y2 = 1, we have

x2+y2+8x4y=5

2a=8a=4

2b=4b=2

r2a2b2=5r2=5+(4)2+(2)2=5+16+4=25

r=5