Correct Answer - Option 1 :
\(\frac{\sqrt{34}}{5}\)
Concept:
General form of the equation of a circle, x2 + y2 + 2gx + 2fy + c = 0
Centre is (-g, -f) or \(\rm \left ( \frac{-\ coefficient \ of \ x}{2},\ \frac{-\ coefficient \ of \ y}{2} \right )\), where g , f and c are constant.
Radius = \(\rm\sqrt{g^{2}+f^{2}-c}\)
Calculation:
Given equation of circle is , 5x2 + 5y2 - 20x - 6y + 15 = 0
⇒ x2 + y2 - 4x - \(\frac{6}{5}\)y + 3 = 0 ....(i)
On compare eq. (i) with standard equation of circle x2 + y2 + 2gx + 2fy + c = 0
We get , g = -2 , f = \(\frac{-3}{5}\) and c = 3
As we know that , radius of circle = \(\rm\sqrt{g^{2}+f^{2}-c}\)
⇒ radius = \(\sqrt{(-2)^{2}+\left ( \frac{-3}{5} \right )^{2}-3}\) = \(\sqrt{4+\frac{9}{25}-3}\)
⇒ radius = \(\frac{\sqrt{34}}{5}\) units.
The correct option is 1.
