If x = a ( t - 1 t ) and y = b ( t + 1 t ) , then dy dx =

Step-by-step solution

aligned & x = a ( t - 1 t ) and y = b ( t + 1 t ) & dx dt = a (1+ 1 t ^2 ) and dy dt = b (1- 1 t ^2 ) & dy dx = b (1- 1 t ^2 ) a (1+ 1 t ^2 ) = ( b a ) ( t ^2-1 t ^2+1 ) aligned Now x = a ( t ^2-1 t ) and y = b ( t ^2+1 t ) ...[From (1)] ( t ^2-1 )= ( x a ) t and ( t ^2+1 )= ( y b )( t ) Eq. (2) becomes d y d x = ( b a ) ( x a )(t) 1 ( y b ) t = b^2 x a^2 y