Length of Tangent, Subtangent, Normal and Subnormal to \[{{\mathbf{y}}^{\mathbf{2}}}\mathbf{= 4ax}\,\,\mathbf{at }\,\mathbf{(a}{{\mathbf{t}}^{\mathbf{2}}}\mathbf{,2at)}\]
Category : JEE Main & Advanced
(1) Length of tangent at \[(a{{t}^{2}},2at)\]\[=2at\,\text{cosec}\psi \]
\[=2at\sqrt{(1+{{\cot }^{2}}\psi )}\] \[=2at\sqrt{1+{{t}^{2}}}\]
(2) Length of normal at \[(a{{t}^{2}},\,2at)=2at\sec \psi \]
\[=2at\sqrt{(1+{{\tan }^{2}}\psi )}\]\[=2a\sqrt{{{t}^{2}}+{{t}^{2}}{{\tan }^{2}}\psi }\] \[=2a\sqrt{({{t}^{2}}+1)}\]
(3) Length of subtangent at \[(a{{t}^{2}},2at)=2at\cot \psi \]\[=2a{{t}^{2}}\]
(4) Length of subnormal at \[(a{{t}^{2}},2at)=2at\tan \psi \]\[=2a\].
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