EllipseHard
Question
The foci of a hyperbola lie at the vertices of the ellipse 
= 1 and its directrixes pass through the foci of the ellipse. The equation of the hyperbola must be :-
= 1 and its directrixes pass through the foci of the ellipse. The equation of the hyperbola must be :-Options
A.
B.
C.
D.None of these
Solution
Let the equation of the hyperbola be
where b2 = a2(e2 - 1)
Then from the given facts
2ae = 2 × 10 ⇒ ae = 10
Also
= 2a′e′
⇒
= 2 × 10 × 
(
is the eccentricity of the ellipse)
We easily get a2 = 60, e2 =
Hence b2 = a2(e2 - 1)
= 60
= 40
⇒ Equation of hyperbola is
where b2 = a2(e2 - 1)
Then from the given facts
2ae = 2 × 10 ⇒ ae = 10
Also
= 2a′e′⇒
= 2 × 10 × (
is the eccentricity of the ellipse)We easily get a2 = 60, e2 =
Hence b2 = a2(e2 - 1)
= 60
= 40⇒ Equation of hyperbola is
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