Consider the ellipse `x^(2)/(tan^(2)alpha)+y^(2)/(sec^(2)alpha)=1` where`alphain(0,pi/2)`. Which of the following quantities would vary as `alpha` varies?

Given the family of hyperbolas x^(2)/(cos^(2)alpha)-y^(2)/sin^(2)alpha=1" for "alphain(0,pi//2) which of the following does not change with varying alpha ?

For the hyperbola (x^(2))/(cos^(2)alpha)-(y^(2))/(sin^(2)alpha)=1;(0

For the hyperbola (x^(2))/(cos^(2) alpha ) - (y^(2))/(sin^(2) alpha ) = 1 , where alpha is a parameter, which of the following remains constant ?

If latus recturn of the ellipse x^(2)tan^(2)alpha+y^(2)sec^(2)alpha=1 is (1)/(2) then alpha(0

if (1+tan alpha)(1+tan4 alpha)=2 where alpha in(0,(pi)/(16)) then alpha equal to

tan^(2)alpha=1-p^(2) then sec alpha+tan^(3)alpha*cos ec alpha

For the hyperbola (x^(2))/(cos^(2)alpha)-(y^(2))/(sin^(2)alpha)=1 which of the following remains constant when varies? (1) eccentricity (2) directrix (3) abscissae of vertices (4) abscissae of foci