Question
If the latus rectum of the ellipse x2 tan2 
+ y2 sec2 = 1 is 
then =
- None
Hint:
find out the length of latus rectum in terms of the trigonometric functions and the equate it with the given numeric value.
The correct answer is:
5π/12
Here, a= 1/tanѲ
b= 1/secѲ
we know that e2 = 1-b2/a2
e2= 1-sin2Ѳ = cos2Ѳ
we know that length of latus rectum = 2b2/a=2a(1-e2)
2a(1-cos2Ѳ)=2asin2Ѳ=1/2
a=1/tanѲ=cot Ѳ= cosѲ/sinѲ
=> length of latus rectum = 2 cosѲ sin2Ѳ/sinѲ
sin2Ѳ = ½
=> 2Ѳ = π/6, 5π/6
Ѳ= π/12, 5π/12
length of latus rectum = 2b2/a=2a(1-e2)
this is used to find the value of alpha
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