Thank you for reporting, we will resolve it shortly
Q.
If the normal to the rectangular hyperbola $x y=c^2$ at the point ' $t$ ' meets the curve again at ${ }^{\prime} t_1{ }^{\prime}$ then $t^3 t_1$ has the value equal to -
Conic Sections
Solution:
Equation of normal of rectangular hyperbola $xy = c ^2$ at $P ( ct , c / t )$ will be
$y-\frac{c}{t}=t^2(x-c t)$
as it also passes through $t_1$
$\Rightarrow c\left(\frac{1}{t_1}-\frac{1}{t}\right)=c t^2\left(t_1-t\right)$
$\Rightarrow t^3 t_1=-1$