If the normal to the rectangular hyperbola $xy = c^{2}$ at the point ' $t$ ' then $t^{3}t_{1}$ has t

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If the normal to the rectangular hyperbola $xy = c^{2}$ at the point ' $t$ ' then $t^{3}t_{1}$ has the value equal to :

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Sol. (b)Slope of normal at $A$$$\begin{matrix} & \ = - \frac{1}{\frac{dy}{dx}} = \frac{x^{2}}{c^{2}} = t^{2} \ & 	ext{~}	ext{of chord}	ext{~}AB \end{matrix}$$$$\begin{matrix} & \ = \frac{c\left( \frac{1}{t} - \frac{1}{t_{1}} ight)}{c\left( t - t_{1} ight)} = \frac{- 1}{tt_{1}} \ \Rightarrow \ t^{2} & \ = - \frac{1}{tt_{1}} \end{matrix}$$$$\Rightarrow \ t^{3}t_{1} = - 1$$

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