Prove that an infinite number of triangles can be inscribed in either of the parabolas y^2=4ax and x^2=4by whose sides touch the other

For the 2 parabolas: y²=4ax and x²=4by intersect at 2 points

A(0,0) and B[ 4*(ab²)^1/3,(4*(a²b)^1/3) ]  which lie on common chord y = (a/b)^1/3*x

for any general point ( at^2,2at) on y²=4ax where t is parameter

and for any general point ( am²,2am) on x²=4ay where m is parameter

there can be infinite points taken on both these parabolas and can form triangles with the common chord

y = (a/b)^1/3*x