EllipseHard
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
View Solution FreeMore Ellipse Questions
The equation of the ellipse whose foci are (± 5, 0) and one of its directrix is 5x = 36, is -...tangent is drawn from point P(- 4, 0) to the ellipse = 1 (a > b) which makes 60o with x-axis. If this tangent intersects...If p and p′ denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis...The circle on SS′ as diameter touches the ellipse then the eccentricity of the ellipse is (where S and S′ ar...The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q. If M is the mid point of the line segment PQ...