Position of a Point With Respect to a Circle
Category : JEE Main & Advanced
A point \[({{x}_{1}},\,{{y}_{1}})\] lies outside, on or inside a circle \[S\equiv {{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] according as \[{{S}_{1}}\equiv x_{1}^{2}+y_{1}^{2}+2g{{x}_{1}}+2f{{y}_{1}}+c\] is positive, zero or negative.
The least and greatest distance of a point from a circle: Let \[S=0\] be a circle and \[A\,({{x}_{1}},\,{{y}_{1}})\] be a point. If the diameter of the circle through A is passing through the circle at P and Q, then \[AP=\ |AC-r|\ =\] least distance; \[AQ=AC+r=\] greatest distance where \['r'\] is the radius and C is the centre of the circle.
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