Correct Answer - Option 1 :
\(\sqrt{\frac{28}{3}}\) units
Concept:
General form of the equation of a circle, x2 + y2 + 2gx + 2fy + c = 0
Radius = \(\rm\sqrt{g^{2}+f^{2}-c}\)
Calculation:
The given equation of circle is , 3x2+ 3y2- 6x+ 12y- 13= 0
⇒ x2+ y2- 2x + 4y - \(\frac{13}{3}\) = 0 ....(i)
On compare with standard equation of circle x2 + y2 + 2gx + 2fy + c = 0
where , g = 1 , f = 2 and c = - \(\frac{13}{3}\)
We know that , radius of circle = \(\rm\sqrt{g^{2}+f^{2}-c}\)
⇒ radius = \(\sqrt{1^{2}+2^{2}-\left ( -\frac{13}{3} \right )}\)
⇒ radius = \(\sqrt{\frac{28}{3}}\) units.
The correct option is 1.
