Q.

For the hyperbola x2cos2 α-y2sin2 α=1  which of the following remains constant when α varies?

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a

directrix

b

abscissae of vertices

c

abscissae of foci

d

eccentricity

answer is A.

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Detailed Solution

x2cos2α-y2sin2α=1 a2=cos2α, b2=sin2α Now e=a2+b2a2 e=cos2α+sin2αcos2α e    =1cosα Now ae=cosα1cosα               =1

 abscissae of foci is constant when 'α' varies.

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