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Question
The circle x2 + y2 + 2gx + 2fy + c = 0 does not intersect x-axis, if
Options
g2 < c
g2 > c
g2 > 2c
none of these
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Solution
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.
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