Subtangent and Subnormal of the Hyperbola
Category : JEE Main & Advanced
Let the tangent and normal at \[P({{x}_{1}},\,{{y}_{1}})\] meet the x-axis at A and B respectively.
Length of subtangent
\[AN=CN-CA={{x}_{1}}-\frac{{{a}^{2}}}{{{x}_{1}}}\].
Length of subnormal
\[BN=CB-CN=\frac{({{a}^{2}}+{{b}^{2}})}{{{a}^{2}}}{{x}_{1}}-{{x}_{1}}\]
=\[\frac{{{b}^{2}}}{{{a}^{2}}}{{x}_{1}}=({{e}^{2}}-1){{x}_{1}}\].
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