Suppose that the foci of the ellipse 
= 1 are (f 1 , 0) and (f 2 , 0) where f 1 > 0 and f 2 < 0. Let P 1 and P 2 be two parabolas with a common vertex at (0, 0) and with foci at (f 1 , 0) and (2f 2 , 0), respectively. Let T 1 be a tangent to P 1 which passes through (2f 2 , 0) and T 2 be a tangent to P 2 which passes through (f 1 ,0). If m 1 is the slope of T 1 and m 2 is the slope of T 2 , then the value of 
is.
Text Solution
Verified by Experts4
(4)
Sol. e 2 = 1 – 
e = 
focii (2, 0) (–2, 0)
p 1 : y 2 = 8x,
y = m 1 x + 
0 = –4m 1 + 
⇒ 
⇒ m 1 = ± 
p 2 : y 2 = –16x
⇒ y = m 2 x 
⇒ 0 = 
⇒ 
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