Question

Find the radius of curvature of a parabola y2=4ax at the origin

Answer 1

The radius of curvature of a parabola y2=4ax at the origin is 2a

To find the radius of curvature of a parabola y2=4ax at the origin:

Y2=4ax

Differentiating both side w.r.t X,

2yy'=4a

Or,y'=2a/y

For (x,y)=(0,0)

Y'=Infinity

So we go for the alternative formula.

Hence, we differentiate both side w.r.t. y

Y2=4ax

2y=4ax'..(1)

Or,x'=y/2a

At (0,0) ,x'=0

Differentiating (1) again we get,

1/2a=X"

We know,

Radius of curvature, r= |(1+x'^2)^3/2|/|X"|

Hence, at (0,0) , r= |1+0|^3/2/|1/2a|=2a

Answer 2

Answer:

Step-by-step explanation: