Question

Radius of the curvature of the curve x=at^2,y=2at

Answer 1

y²=4ax............................1

dy/dy=2a/y

At the point (at^2 , 2at) dy/dx=1/t1

Equation of normal at the point (at^2 , 2at) is

(y-2at)(1/t)+x-at^2=0

y+xt=2at+at³...........2

If normal point agian meets at

(af^2,2af),then this point will satisfy (2)

2af+aft=2at+at³.

a(f-t)[2+t(f+t)]=0

2+t(f+t)=0

or f=-t - 2/t .