Question Number 51901 by peter frank last updated on 31/Dec/18
$${Prove}\:{that}\:{the}\:{two}\: \\ $$ $${parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{ax}\:{and} \\ $$ $${y}^{\mathrm{2}} =\mathrm{4}{c}\left({x}−{b}\right)\:{cannot} \\ $$ $${have}\:{a}\:{common}\:{normal} \\ $$ $${other}\:{than}\:{the}\:{axis}\:{unless} \\ $$ $$\frac{{b}}{{a}−{c}}>\mathrm{2} \\ $$