1) If the eccentricity of the hyperbola x2-y2 cosec2α= 25 is √5 times the eccentricity of the elipse x2 cosec2α+y2=5 then α is equal to; A) tan−1√2 B) sin−1√34 C) tan−1√25 D) sin−1√25 Answer: Option AExplanation:Eccentrcity of x225+y225sin2α=1 is √1+sin2α Eccentrcity of x25sin2α+y25=1 is √1−sin2α Given, √1+sin2α=√5√1−sin2α ⇒ sin2α=23 ⇒ α=sin−1√23=tan−1√2