Correct Answer - Option 2 : 1/2
Concept:
The standard equation of a circle is x2 + y2 + 2gx + 2fy + c = 0 with centre at (- g, - f) and radius \(r = \sqrt {{g^2} + {f^2} - c}\)
Calculation:
Given: Equation of circle is x2 + y2 + x + c = 0 and it passes through origin.
⇒ The point (0, 0) will satisfy the equation x2 + y2 + x + c = 0.
⇒ c = 0.
Hence, the equation of circle is x2 + y2 + x = 0. Now by comparing it with the standard equation of circle x2 + y2 + 2gx + 2fy + c = 0 we get, g = 1 / 2, f = 0 and c = 0.
So the radius of the circle x
2 + y
2 + x = 0 is
\(r = \sqrt {\frac{1}{4} + 0 - 0} = \frac{1}{2}\)