The distance, from the origin, of the normal to the curve, x=2cost+2tsint, y=2sint-tcost at t=π/4, is

The correct option is A
2x=2cost+2tsint
dx/dt=2tcost+2sint-sint=2tcost
y=2sint-tcost
dy/dt=2cost+2tsint-cost=2tsint
dy/dx=2tsint/2tcost(t=π/4)
dy/dx=1
dx/dy=-1 for slope of normal.
x(π/4)=2cos(π/4)+2.(π/4)sin(π/4)=√2(1+π/4)
y(π/4)=2sin(π/4)-.(π/4)cos(π/4)=√2(1-π/4)
Equation of normal with given point
x+y-√2=0
d=(2√2)/√2=2