Questions
If the latus rectum of a hyperbola subtend an angle of 60° at the other focus, then eccentricity of the hyperbola is
a
2
b
3+12
c
23
d
3
detailed solution
Correct option is D
Let the equation of the hyperbola be x2a2−y2b2=1 F1(−ae,0),F2(ae,0) be the foci, e being the eccentricity.Let LF2L′, the latus rectum subtend an angle of 60° at F1, then slope of LF1 is tan 300. So tan 30∘=b2/a2ae⇒ 13=a2e2−12a2e=e2−12e⇒ e2−1=23e⇒e−132=1+13⇒ e−13=23⇒e=3Talk to our academic expert!
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[.] denotes Greatest integer function)
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