wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If PQ is a double ordinate of the hyperbola x2a2y2b2=1 such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then
(where e is the eccentricity of the hyperbola)

A
1<e<23
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
e=23
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1<e<32
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
e>23
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D e>23
Given hyperbola is x2a2y2b2=1
The coordinates of P and Q are
P(asecθ,btanθ)Q(asecθ,btanθ)
As OPQ is equilateral, so
tan30=btanθasecθ3ba=cosec θ3b2a2=cosec2θ3(e21)=cosec2θe2=cosec2θ3+1
As cosec2θ>1, so
e2>43e>23

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Parametric Representation-Hyperbola
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon