Maths-
General
Easy
Question
If latus rectum of ellipse x2tan2
+ y2sec2 = 1 is 
then {0 < < 
/4} is equal to
- None of these
Hint:
use the definition of ellipse to find out the eccentricity and length of latus rectum. then use trigonometric functions to simplify the expression.
The correct answer is:
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
the focal chord that is perpendicular to the major axis of the ellipse is called the latus rectum of the ellipse.
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