The Cartesian form of the curve given by x= a 2 (t+ 1 t ) , y= a 2 (t- 1 t ), t is a parameter, is

Step-by-step solution

aligned & x= a 2 (t+ 1 t ).....(i) & y= a 2 (t- 1 t ).....(ii) aligned aligned & Eq. (i) )^2-(i i)^2 x^2-y^2 & = a^2 4 (t+ 1 t )^2- a^2 4 (t- 1 t )^2 & = a^2 4 (t^2+ 1 t^2 +2-t^2- 1 t^2 +2 ) & = a^2 4 (2+2)= a^2 4 4 & x^2-y^2=a^2 aligned