EllipseHard
Question
For the hyperbola 
= 1, which of the following remains constant when α varies?
= 1, which of the following remains constant when α varies?Options
A.eccentricity
B.directrix
C.abscissae of vertices
D.abscissae of foci
Solution
a2 = cos2 α and b2 = sin2 α
coordinates of focii are (± ae, 0)
∴ b2 = a2(e2 - 1) ⇒ e = sec α.
Hence abscissae of foci remain constant when α varies.
coordinates of focii are (± ae, 0)
∴ b2 = a2(e2 - 1) ⇒ e = sec α.
Hence abscissae of foci remain constant when α varies.
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