If the eccentricity of the hyperbola x2 – y2 sec2 = 5 is times the eccentricity of the ellipse x2 sec2 +y2 = 25, then =

Given: e1 and e2 are respectively the eccentricities of x2 – y2 sec2 α = 5 and x2 sec2 α + y2 = 25 respectively


To find: value of α


x2 – y2 sec2 α = 5





Eccentricity(e) of hyperbola is given by,











Therefore,




For ellipse:


x2 sec2 α + y2 = 25






Eccentricity(e) of ellipse is given by,








Therefore,




According to question:


Eccentricity of given hyperbola is time eccentricity of given ellipse



From (1) and (2):



Squaring both sides:


1 + cos2 α = 3(1 – cos2 α)


1 + cos2 α = 3 – 3 cos2 α


3 cos2 α + cos2 α = 3 – 1


4 cos2 α = 2




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