Director Circle
Category : JEE Main & Advanced
The locus of the point of intersection of two perpendicular tangents to a circle is called the Director circle.
Let the circle be \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then equation of director circle is \[{{x}^{2}}+{{y}^{2}}=2{{a}^{2}}\].
Obviously director circle is a concentric circle whose radius is \[\sqrt{2}\] times the radius of the given circle.
Director circle of circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+2c-{{g}^{2}}-{{f}^{2}}=0\].
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