4Ans given is A C D
Consider an ellipse x2/sec2a + y2/tan2 a = 1 ,0<a<pi/4
with foci S1 & S2 . Let M be a point on the y-axis such that OM = OS1 , where O is origin.
Which of the following r correct?
(A)M lise inside the ellipse
(B) M lies outside the ellipse
(C)foci lies on x = 1,-1
(D)latus rectum lies in the interval (0,1/√2 )
NOT MY DOUBT
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4 Answers
1Since 0<a<pi/4,
The equation of the largest possible ellipse should be :
x2/2 + y2/1 = 1
Where focii wil be less than (-√2,√2)
In option C, it is given -1,1 so the rest of the real numbers are not included.
Since OM = OS1, it is lesser than length of minor axis. (2 x 1), hence M lies inside ellipse.
If focii are in interval (-√2,√2) then latus rectum interval should also have a negative limit. Since the interval given is (0,1/√2) hence option D is also wrong.
Hence correct answer is A
1Well i had told ya its A nd C..... u made me disprove myself !!!! had to sit fr hours fr this!!! [5]
4No Ankur
D is also right as latus rectum doesn't lie only in (0,1/√2) but lies in (0,1/√2)
(U understood the difference na??)