Question

The slope of the normal to the curve x=a(t-sint),y=a(1-cost) at t=90°

Answer 1

Slope = Dy/dx

x= a(t-sint)

diff with respect to 't'

dx/dt= a(1-cost)

y = a(1- cost)

diff with respect to 't'

dy/dt = a(sint)

dy/dx = a(sint)/a(1-cost)

dy/dx= sint/1-cost

(Dy/dx)t=90° = sin90°/ 1- cos 90°

= 1/1-0

=1/1 =1

Therefore, slope of normal to the curve is 1

Answer 2

Answer:

dy/dt=sint

dx/dt=1-cost

dy/dt=sint/1-cost

        =sin(90)/1-cos(90)

        =1/1-0

         =1