Question

The circle x² + y² + 2gx + 2fy + c = 0 does not intersect x-axis, if

पर्याय

• g² < c

• g² > c

• g² > 2c

• none of these

Answer 1

g² < c

Given:
x² + y² + 2gx + 2fy + c = 0   ...(1)
The given circle intersects the x-axis.
The equation of circle becomes x² + 2gx + c = 0.    ...(2)
Solving equation (2):
∴  Discriminant, D = \[\sqrt{4 g^2 - 4c} \geq 0\]

\[\Rightarrow 4 g^2 - 4c \geq 0\]

\[ \Rightarrow g^2 - c \geq 0\]

\[ \Rightarrow g^2 \geq c\]

Hence, if \[g^2 < c\],then the given circle will not intersect the x-axis.