EllipseHard
Question
An ellipse intersects the hyperbola 2x2 - 2y2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinates axes, then
Options
A.equation of ellipse is x2 + 2y2 = 2
B.the foci of ellipse are (± 1, 0)
C.equation of ellipse is x2 + 2y2 = 4
D.the foci of ellipse are (± √2, 0)
Solution
Ellipse and hyperbola will be confocal
⇒ (± ae, 0) ≡ (±1, 0)
⇒
≡ (±1, 0)
⇒ a = √2 and e =
⇒ b2 = a2 (1 - e2) ⇒ b2 = 1
∴ Equation of ellipse
= 1.
⇒ (± ae, 0) ≡ (±1, 0)
⇒
≡ (±1, 0)⇒ a = √2 and e =
⇒ b2 = a2 (1 - e2) ⇒ b2 = 1
∴ Equation of ellipse
= 1.Create a free account to view solution
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