If is the angle made by the normal drawn to the curve x = e ^ t t , y = e ^ t t at the point (1,0) , with the X -axis, then =

Step-by-step solution

x=e^t t, y =e^t t d x d t =e^t( t- t) and d y d t =e^t( t+ t) Now, d y d x = d y d t d x d t = e^t( t+ t) e^t( t- t) d y d t = t+ t t- t At point (1,0): x=1 & y=0 aligned & y=0 e^t t=0 & t=0 t=0 aligned Now, slope of normal is aligned & m=- 1 d y d x =- t- t t+ t & m= 0- 0 0+ 0 = -1+0 0+1 =-1 & =-1 = 3 4 aligned