For the hyperbola (x^(2))/(cos^(2)alpha)...

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

directrix

vertices

foci

eccentricity

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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?

P( asec alpha, b tan alpha ) and Q (a sec beta, b tan beta) are two given points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1. Show that the equation of the chord PQ is (x)/(a) cos (alpha - beta)/(2) - (y)/(b) sin (alpha + beta)/(2) = cos (alpha+beta)/(2).

(x^(2))/(cos^(2)alpha)-(y^(2))/(sin^(2)alpha) = 1 (0 lt alpha lt (pi)/(2)) is the equation of a hyperbola, then which of the following(s) is /are depend(s) on alpha -

If 0 lt alpha lt (pi)/(2) , then which of the following is independent of alpha in the case of the hyperbola (x^(2))/(cos^(2)alpha) - (y^(2))/(sin^(2)alpha) = 1 ?

If (alpha +beta ) and (alpha - beta ) are the eccentric angles of the points P and Q respectively on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 show that the equation of the chord PQ is (x)/(a) cos alpha+(y)/(b)sin alpha = cos beta .

show that (1-sin^2 alpha)(1-cos^2 alpha)(1+cot^2 alpha)(1+tan^2 alpha) = 1.

(sin alpha)/(sin 2x) +(cos alpha)/(cos 2x) =2

If sin2 alpha = A sin 2(alpha + beta), A ne 0, "then" Which values of the following are not equal to tan2(alpha + beta) ?

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