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Question : 56 of 160
Marks:
+1,
-0
Solution:
Given ellipse,
‌+‌=1 Let eccentricity of ellipse be '
e′ Then
b2=a2(1−e2) Here,
b2=12,a2=16 ∴‌‌12=16(1−e2) 1−e2=‌ or
e2=1−‌=‌ or
e=‌ If
α,β are the eccentric angles of the ends of a focal chord of the ellipse, then eccentricity is given by
e=‌ Here,
α=‌,β=θ, and
e=‌ ‌=‌ Multiplying in
Nr and
Dr by
2‌sin(‌) and
2‌sin‌A‌cos‌A=sin‌2‌A} ‌=‌| sin‌+sin‌θ |
| sin‌‌cos‌θ+cos‌‌sin‌θ |
‌‌cos‌θ+‌‌sin‌θ=√3+2‌sin‌θ or
‌‌‌‌cos‌θ=‌‌sin‌θ+√3 or
cos‌‌cos‌θ−sin‌‌sin‌θ=1 On comparing both sides, we get
tan‌θ=−√3
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