# Find radius of the circle: 3x2+ 3y2- 6x+ 12y- 13= 0

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Find radius of the circle: 3x2+ 3y2- 6x+ 12y- 13= 0
1. $\sqrt{\frac{28}{3}}$ units
2. $\sqrt{\frac{13}{3}}$ units
3. ${\frac{\sqrt28}{3}}$ units
4. ${\frac{\sqrt13}{2}}$ units

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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.