Intercepts on the Axes
Category : JEE Main & Advanced
The lengths of intercepts made by the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] on \[X\] and \[Y\] axes are \[2\sqrt{{{g}^{2}}-c}\] and \[2\sqrt{{{f}^{2}}-c}\] respectively.
Therefore,
(i) The circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] cuts the x-axis in real and distinct points, touches or does not meet in real points according as \[{{g}^{2}}>,=\,\ \text{or}\ \,<c\].
(ii) Similarly, the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] cuts the y-axis in real and distinct points, touches or does not meet in real points according as \[{{f}^{2}}>,=\,\ \text{or}\ \,<c\].
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