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  • The normal to the rectangular hyperbola  at the point ‘t’ meets the

The normal to the rectangular hyperbola \mathrm{x y=c^2} at the point ‘t’ meets the curve again at a point ‘t’, then

Option: 1

\mathrm{t^3 t^{\prime}=-1}


Option: 2

\mathrm{t^2 t^{\prime}=-1}


Option: 3

\mathrm{t t^{\prime}=-1}


Option: 4

none of  these

 


Answers (1)

best_answer

\mathrm{\text { Normal at ' } t \text { ' for } x y=c^2}

\mathrm{\text { is } t y=t^3 x+c-c t^4 \text { or } x t^3-t y+c-c t^4=0}       ...[i]

Equation of line joining \mathrm{t \text { and } t^{\prime}}  is 

\mathrm{\begin{gathered} y-\frac{c}{t}=\frac{c}{t^{\prime}-\frac{c}{t}} \frac{c t}{c t^{\prime}-c t}(x-c t) \\ \Rightarrow \quad x+y t t^{\prime}-c\left(t+t^{\prime}\right)=0 \end{gathered}}

[on simplification]

\mathrm{\therefore \quad \frac{t^3}{1}=-\frac{1}{t^{\prime}}=\frac{1-t^4}{-\left(t+t^{\prime}\right)} \Rightarrow t^3 t^{\prime}=-1}

 

Posted by

Pankaj Sanodiya

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