JEE Main 2020 — Hyperbola Question with Solution
From: JEE Main 2020 (Online) 3rd September Evening Slot
Question
Let e1
and e2
be the eccentricities of the
ellipse,
(b < 5) and the hyperbola,
respectively satisfying e1e2 = 1. If
and are the distances between the foci of the
ellipse and the foci of the hyperbola
respectively, then the ordered pair (, ) is equal to :
(b < 5) and the hyperbola,
respectively satisfying e1e2 = 1. If
and are the distances between the foci of the
ellipse and the foci of the hyperbola
respectively, then the ordered pair (, ) is equal to :
Choose an option
Show full solutionCorrect option: A
Correct answer
A(8, 10)
Step-by-step explanation
For ellipse
Let e1 is eccentricity of ellipse
b2 = 25 (1 ) ........(1)
Again for hyperbola
Let e2 is eccentricity of hyperbola.
......(2)
by (1) & (2)
Now e1 . e2 = 1 (given)
or e1 = e2 =
Now distance between foci is 2ae
Distance for ellipse =
Distance for hyperbola =
(, ) (8, 10)
Let e1 is eccentricity of ellipse
b2 = 25 (1 ) ........(1)
Again for hyperbola
Let e2 is eccentricity of hyperbola.
......(2)
by (1) & (2)
Now e1 . e2 = 1 (given)
or e1 = e2 =
Now distance between foci is 2ae
Distance for ellipse =
Distance for hyperbola =
(, ) (8, 10)
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