Question

determine the circle of curvature at the origin of the parabola y=kx+2x²​

Answer 1

Answer:

]Answer

By formula,  radius of curvature for the curve in the form of y=f(x) is given as R=∣∣∣∣∣dx2d2y∣∣∣∣∣[1+(dxdy)2]3/2

Here, y=ax2,   dxdy=2ax,   dx2d2y=2a

Thus, R=∣2a∣[1+(2ax)2]3/2

For x=0,R=2a1