Intersection of a Line and a Circle
Category : JEE Main & Advanced
The length of the intercept cut off from the line \[y=mx+c\] by the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] is \[2\sqrt{\frac{{{a}^{2}}(1+{{m}^{2}})-{{c}^{2}}}{1+{{m}^{2}}}}\].
(i) If \[{{a}^{2}}(1+{{m}^{2}})-{{c}^{2}}>0\], line will meet the circle at two real and different points.
(ii) If \[{{c}^{2}}={{a}^{2}}(1+{{m}^{2}})\], line will touch the circle.
(iii) If \[{{a}^{2}}(1+{{m}^{2}})-{{c}^{2}}<0\], line will meet the circle at two imaginary points.
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