Dear Candidate,

I will try to solve your query. But be aware that we are limited by our answering options & you can search the internet for detailed step by step method for your better understanding.

Let X=a³ × cos³(alpha) & y=a³ × sin³(alpha) now differentiate both the terms wrt (alpha)

You will get dy/dx = -tan(alpha) & similarly

d²x/d²y = -sec²(alpha) × d(alpha)/dx

Radius of curvature = 3a(xy)

Thanks. Hope it helped you.