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For a curve y = e^{x}, at any pont (x_o, y_o)  on it, difference of square of length of tangent and square of length of y_o equals 

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As we have learned

Length of Tangent -

L_{T}=\frac{y}{y'}\sqrt{1+y'^{2}}

- wherein

Where Where\:\:y'=\frac{dy}{dx}

 

 

Length of tangent at (x,y) =\frac{y}{y'}\sqrt{1+(y')^{2}}

\Rightarrow Length = \frac{e^{x0}}{e^{x0}}\sqrt{1+(e^{x0})^{2}}= \sqrt{1+ (e^{x0})^{2}}= \sqrt{1+(y_{0})^{2}}

\Rightarrow (length..of ..tangent)^{2}- (y_{0})^{2}=1

 

 

 

 


Option 1)

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Option 2)

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Option 3)

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Option 4)

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Himanshu

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