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Question

For the hyperbola ,x2cos2a-y2sin2a=1which of the following remains constant when ɑ varies?


A

Eccentricity

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B

Directrix

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C

Abscissae of vertices

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D

Abscissae of foci

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Solution

The correct option is D

Abscissae of foci


Explanation for the correct options:

Finding the value.

In hyperbola:

b2=a2(e21)

sin2a=cos2a(e2-1)

tan2a+1=e2

e2=sec2a

So, Vertices (±cosα,0)

Coordinate of foci are (±ae,0)(±1,0)

If ɑ varies then the abscissa of foci remain constant.

Hence, Option(D) is correct.

Explanation for the incorrect options:

If ɑ varies then Eccentricity, Directrix and Abscissae of vertices does not remain constant.

Hence, Option(A),(B) and (C) are incorrect.


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