3 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.First the curve:
1. Differentiate to get the slope at x=0
2. Since this is symmetric in x and y, it will have a symmetry about x=y
3. Easy to notice, it will be symmetric for all 4 quadrants. (as replacing x or y with -x or -y doesn't change the value of x^(2/3) or y^(2/3))
As for the area, the parametric points of an astroid are asin^3(theta) and acos^3(theta).