Please,help me with this problem. 1. The problem statement, all variables and given/known data Prove that the two families of parabolas [tex]y^2=4a(a-x),a>0[/tex] and [tex]y^2=4b(b+x),b>0[/tex] form an orthogonal net. Specifically, check that for any a, b > 0 these two parabolas are perpendicular to each other at the points where they intersect. 3. The attempt at a solution Their tangent spaces at point [tex](x_0,y_0)[/tex] are [tex]2y_0(y-y_0)+4a(x-x_0)=0[/tex] [tex]2y_0(y-y_0)-4b(x-x_0)=0[/tex] If they are perpendicular then we have [tex]4y_0^2-16ab=0\Rightarrow y_0^2=4ab[/tex] from the equations of parabolas we have [tex]y_0^2=4a(a-x_0)[/tex] [tex]y_0^2=4b(b+x_0)[/tex] if we substitute [tex]x_0[/tex] [tex]y_0^2=4ab[/tex] So they are perpendicular.