For the hyperbola `x^2/ cos^2 alpha - y^2 /sin^2 alpha = 1 which of the following remains constant when alpha varies?

Options

A. Eccentricity
B. Abscissa of foci
C. Directrix
D. Vertex

Answer

B

Explanation

`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.`