The distance from the origin of the normal to the curve `x=2cos t+2tsint `, `y=2sint-2tcost` , at `t=(pi)/4` is

The distance, from the origin, of the normal to the curve, x = 2 cos t + 2t sin t, y = 2 sin t - 2t "cos t at t" = (pi)/(4) , is :

The distance between the origin and the normal to the curve y=e^(2x)+x^(2) at x=0 is

The length of the normal at t on the curve x=a(t+sint), y=a(1-cos t), is

Find the equations of the tangent and normal to the curve x=sin3t.,y=cos2t at t=(pi)/(4)

Find the equations of the tangent and normal to the curve x = a sin 3t, y = cos 2 t " at " t = (pi)/(4)

If x=2cost-cos2t , y=2sint-sin2t ,then at t=(pi)/(4) , (dy)/(dx)=

The slope of the tangent to the curve x=2 sin ^(3) t, y=3 cos ^(3) t " at " t= (pi)/(4) is

Prove that all normals to the curve x=acost+a tsint ,\ \ y=asint-a tcost are at a distance a from the origin.