For the Hyperbola x2/cos2α - y2/sin2α = 1,  which of the following remains constant when a varies ?

(a) abscissae of vertices

(b) abscissae of foci

(c) eccentricity 

(d) directrix.

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1 Answers

(b) : ∵ b2 = a2(e 2 – 1) => sin2α = cos2α (e2 – 1)
=> tan2 α + 1 = e2 => e2 = sec2α
Vertices ≡ (±cosα, 0)
Coordinate of focii are (±ae, 0) ≡ (±1 ,0)
=> if a varies then the abscissa of foci remain constant.

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