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))>2


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

$P r o v e t h a t t h e t w o$ $p a r a b o l a y^{2} = 4 a x a n d$ $y^{2} = 4 c (x - b) c a n n o t$ $h a v e a c o m m o n n o r m a l$ $o t h e r t h a n t h e a x i s u n l e s s$ $\frac{b}{a - c} > 2$
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