Correct Answer - Option 4 : (-2,
\(\frac{3}{2}\) ) and
\(\frac{\sqrt{11}}{2}\) units.
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 2x2+ 2y2 + 8x- 6y+ 7 = 0
⇒ x2 + y2 + 4x - 3y + \(\frac{7}{2}\) = 0 ....(i)
On compare eq. (i) with standard equation of circle x2 + y2 + 2gx + 2fy + c = 0
We get , g = 2 , f = \(\frac{-3}{2}\) and c = \(\frac{7}{2}\)
As we know that centre of circle is (-g, -f)
⇒ centre (-2, \(\frac{3}{2}\) ) .
And radius of circle = \(\rm\sqrt{g^{2}+f^{2}-c}\)
⇒ radius = \(\sqrt{2^{2}+\left ( \frac{-3}{2} \right )^{2}-\frac{7}{2}}\) = \(\sqrt{4+\frac{9}{4}-\frac{7}{2}}\)
⇒ radius = \(\frac{\sqrt{11}}{2}\) units.
The correct option is 4.