Let the curve be represented by x=2( t + t t ), y=2( t - t t ) . Then normal at any point ' t ' of the curve is at a distance of units from the origin.

Step-by-step solution

array ll & x=2( t + t t ) & d x dt =2(- t + t + t t )=2 t t & y=2( t - t t ) & d y dt =2( t - t + t t )=2 t t & d y ~d x = d y dt d x dt = 2 t t 2 t t = tan t & Slope of normal =- 1 d y ~d x =- 1 t =- t t array Equation of the normal is aligned & y-2( t-t t)=- t t [x-2( t+t t)] & y t -2 ^2 t +2 t t t & =-x t+2 ^2 t+2 t t t & x t +y t =2 ( ^2 t + ^2 t ) & x t +y t =2 & Distance from origin = | -2 ^2 t + ^2 t |=2 units & aligned