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For the hyperbola x^2/ cos^2 alpha - y^2...

For the hyperbola `x^2/ cos^2 alpha - y^2 /sin^2 alpha = 1;(0 lt alphalt pi/4)`. Which of the following remains constant when alpha varies?

A

Eccentricity

B

Abscissa of foci

C

Directrix

D

Vertex

Text Solution

Verified by Experts

The correct Answer is:
B
`e^(2)=1+(b^(2))/(a^(2))=1+(sin^(2)alpha)/(cos^(2)alpha)=(1)/(cos^(2)alpha)`
`a^(2)=cos^(2)alpha`
`therefore" "a^(2)e^(2)=1`
Hence, the foci are `(pmae, 0)-=(pm1,0)`, which are independent of `alpha.`
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