If the parabolas y 2 = 4b(x – c) and y 2 = 8ax have a common normal, then which one of the following is a valid choice for the ordered triad (a, b, c) ?
Text Solution
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Sol. Normal to there 2 curves are
y = m(x – c) – 2bm – bm 3
y = mx – 4am – 2am 3
If they how a common normal
(c + 2b) m + bm 3 = 4am + 2am 3
⇒ c + 2b – 4a = (2a – b) m 2 (m = 0 corresponds to axis)
⇒ m 2 = 
– 2 > 0
> 2
According to the question answer is (1,2,3,4) but my be in question they want common normal other than x-axis, hence answer is
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