EllipseMedium
Question
If a hyperbola passes through the focus of the ellipse
= 1 and its transverse and conjugate axes coincide with the major and minor axes of the ellipse, and the product of eccentricities is 1, then
= 1 and its transverse and conjugate axes coincide with the major and minor axes of the ellipse, and the product of eccentricities is 1, thenOptions
A.the equation of hyperbola is 
= 1
= 1B.the equation of hyperbola is 
= 1
= 1C.focus of hyperbola is (5, 0)
D.focus of hyperbola is(5√3, 0)
Solution
Eccentricity of ellipse = 
Eccentricity of hyperbola =
and it passes through (± 3, 0)
⇒ its equation
= 1
where 1 +
⇒ b2 = 16
⇒
= 1 and its foci are (± 5, 0).
Eccentricity of hyperbola =
and it passes through (± 3, 0)⇒ its equation
= 1 where 1 +
⇒ b2 = 16 ⇒
= 1 and its foci are (± 5, 0).Create a free account to view solution
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