Exercises

01

A self-orthogonal family

Show that this family of curves is orthogonal to itself: $y^2=4c(x+c)$. (Hint: divide the curves into two families, one with $c>0$ and the other with $c<0$.)
Here’s a picture showing the curves for $c=0.5,1,2$ (opening rightward) and $c=-1,-2$ (opening leftward).