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+1 vote
41.9k views
in Mathematics by (53.1k points)

If the eccentricity of the hyperbola x2 − y2 sec2θ = 5 is √3 times the eccentricity of the ellipse x2 sec2θ + y2 = 25 then one of the value of θ is

(a)  π/2

(b)  π/4

(c)  π/3

(d)  π/6

1 Answer

+2 votes
by (53.3k points)
selected by
 
Best answer

Correct option (b)  π/4

Explanation :

x2/5 - y2/5cos2θ = 1

and the ellipse is

x2/25 cos2θ + y2/25 = 1

Let e1 and e2 be the eccentricities of the hyperbola and the ellipse. Therefore

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