The normal to the rectangular hyperbola x y=c² at the point ' ' ' meets the curve again at a point ^ t^ , such that

Step-by-step solution

Equation of normal at (c t, c / c t) is y t-x t³-c+c t⁴=0 If it passes through any point say Q having its coordinates as ' t ' i.e., ( ct ^ c / t ^ ) The coordinates must satisfy the equation. Hence, we get c t^ t-c t^ t³-c+c t⁴=0 t-t^ 2 t³-t^ +t^ t⁴=0 Factorizing, we get, (t^ t³+1 ) (t-t^ )=0 Hencet ^ t³+1=0 or t^ t³=-1 as t t^