Correct Answer - Option 2 : 2√17
Concept:
The general second degree equation of a circle in x and y is given by: x2 + y2 + 2gx + 2fy + c = 0 with centre (-g, -f) and radius
\(\rm r = \sqrt {{g^2} + {f^2} - c} \)
Calculation:
Given: 2x2 + 2y2 + 24x + 24y + 8 = 0
⇒ 2 (x2 + y2 + 12x + 12y + 4) = 0
⇒ x2 + y2 + 12x + 12y + 4 = 0 are equation of circle with centres C and radius r
By comparing the equation of the circle with the equation x 2 + y2 + 2gx + 2fy + c = 0 we get
g = 6, f = 6 and c = 4
As we know, radius = \(\rm r = \sqrt {{g^2} + {f^2} - c} \)
\(\rm r = \sqrt {{36} + {36} - 4} \)
r = 2√17 unit
∴ The radius of circle is 2√17
