Differentiation of parametric and implicit functions

There are 3 NRICH Mathematical resources connected to Differentiation of parametric and implicit functions
Folium of Descartes
problem
Favourite

Folium of Descartes

Age
16 to 18
Challenge level
filled star filled star filled star
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
Squareness
problem
Favourite

Squareness

Age
16 to 18
Challenge level
filled star filled star filled star
The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
Implicitly
problem

Implicitly

Age
16 to 18
Challenge level
filled star filled star empty star
Can you find the maximum value of the curve defined by this expression?