Equation of Pair of Tangents \[\mathbf{S}{{\mathbf{S}}_{\mathbf{1}}}\mathbf{=}{{\mathbf{T}}^{\mathbf{2}}}\]
Category : JEE Main & Advanced
Pair of tangents: The equation of pair of tangents PA and PB is \[S{{S}_{1}}={{T}^{2}}\],
where \[S\equiv \frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}-1\]
\[{{S}_{1}}\equiv \frac{x_{1}^{2}}{{{a}^{2}}}+\frac{y_{1}^{2}}{{{b}^{2}}}-1\]
\[T\equiv \frac{x{{x}_{1}}}{{{a}^{2}}}+\frac{y{{y}_{1}}}{{{b}^{2}}}-1\]
Director circle: The director circle is the locus of points from which perpendicular tangents are drawn to the ellipse.
Hence locus of \[P({{x}_{1}},{{y}_{1}})\]i.e., equation of director circle is \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\].
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