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The radius of the circle x2 + y2 + x + c = 0 passing through the origin is
1. 1/4
2. 1/2
3. 1
4. 2
5. None of these

1 Answer

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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 x2 + y2 + x = 0 is \(r = \sqrt {\frac{1}{4} + 0 - 0} = \frac{1}{2}\)

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