Prove-that-the-two-parabola-y-2-4ax-and-y-2-4c-x-b-cannot-have-a-common-normal-other-than-the-axis-unless-b-a-c-gt-2-

Question Number 51901 by peter frank last updated on 31/Dec/18

P r o v e t h a t t h e t w o

p a r a b o l a y^{2} = 4 a x a n d

y^{2} = 4 c (x - b) c a n n o t

h a v e a c o m m o n n o r m a l

o t h e r t h a n t h e a x i s u n l e s s

\frac{b}{a - c} > 2