If `x=t^(2)` and `y=2t` then equation of the normal at `t=1` is

If x=t^(2) and y=2t at t=1 is

x-2=t^(2),y=2t are the parametric equations of the parabola-

Show that the locus represented by x = 1/2 a (t + 1/t) , y = 1/2 a (t - 1/t) is a rectangular hyperbola. Show also that equation to the normal at the point 't' is x/(t^(2) + 1) + y/(t^(2) - 1) = a/t .

Find the equation of the tangent and the normal at the point 't,on the curve x=a sin^(3)t,y=b cos^(3)t

Find the equations of the tangent and the normal at the point ' t ' on the curve x=a\ s in^3t , y=b\ cos^3t .

Find the equation of the tangent and the normal at the point 't' on the curve x=a(t+sint), y=a(1-cost)

The parametric equation of a parabola is x=t^(2)+1,y=2t+1. Then find the equation of the directrix.

Find the equations of the tangent and the normal to the curve x=a t^2,\ \ y=2a t at t=1 .

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 the normal to the curve x y=c^2 at (c t ,\ c//t) at the indicated points.