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Question

At some point P on the ellipse, the segment SS1 subtends a right angle, then its eccentricity is

A
e=22
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B
e<12
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C
e>12
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D
32
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Solution

The correct option is C e>12
m1=(bsinθ0acosθl)
m2=(bsinθ0)acosθ+al
m1m2=1
b2sin2θa2cos2θa2l2=1
a2(1l2)sin2θ+a2cos2θa2l2=0

1=l2(1+sin2θ)
l2=1sin2θ+1
l>1sin2θ+1
e>12(maxn value of sin2θ+1=2)

59664_36806_ans.JPG

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