Find the equation of tangent and normal to the curve `x=(2a t^2)/((1+t^2)),y=(2a t^3)/((1+t^2))` at the point for which `t=1/2dot`

(i) Find the equation of tangent to curve y=3x^(2) +4x +5 at (0,5) (ii) Find the equation of tangent and normal to the curve x^(2) +3xy+y^(2) =5 at point (1,1) on it (iii) Find the equation of tangent and normal to the curve x=(2at^(2))/(1+t^(2)) ,y=(2at^(2))/(1+t^(2)) at the point for which t =(1)/(2) (iv) Find the equation of tangent to the curve ={underset(0" "x=0)(x^(2) sin 1//x)" "underset(x=0)(xne0)" at "(0,0)

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 equation of normal to the curves x=t^(2),y=2t+1 at point

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.

Find the equation of normal to the curve x = at^(2), y=2at at point 't'.

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

The equation of tangent to the curve x=(1)/(t), y=t-(1)/(t) at t=2 is

Equation of the tangent and normal to the curve x=t^(2)+3t-8, y=2t^(2) -2t-5 at the point t=2 it are respectvely