Correct Answer - Option 3 : a point
Concept:
We know that eqn of circle is –
x2 + y2 + 2gx + 2fy + c = 0 …….(1)
whose, centre = (-g, -f) and radius = \(\sqrt {{g^2} + {f^2} - c} \)
Calculation:
Given eqn- \({x^2} + {y^2} - x - 3y + \frac{5}{2} = 0\)
On comparing with eqn (1) we get –
2gx = -x, 2fy = -3y,
\(c = \frac{5}{2},g = - \frac{1}{2},\;f = \; - \frac{3}{2}\)
Then, Centre = \(\left( {\frac{1}{2},\frac{3}{2}} \right)\)
Radius = \(\sqrt {{{\left( { - \frac{1}{2}} \right)}^2} + {{\left( { - \frac{3}{2}} \right)}^2} - \left( {\frac{5}{2}} \right)} \)
\( = \sqrt {\frac{1}{4} + \frac{9}{4} - \frac{5}{2}} \)
Radius = \(\sqrt {\frac{{1 + 9 - 10}}{4}} = 0\)
Thus, we can say that a circle whose radius is zero represents a point.