wiz-icon
MyQuestionIcon
MyQuestionIcon
13
You visited us 13 times! Enjoying our articles? Unlock Full Access!
Question

The foci of the ellipse x216+y2b2=1 and the hyperbola x2144y281=125 coincide then b2= ?

A
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
7
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
9
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 7
Given hyperbola is, x2144y281=125
x2144/25y281/25=1
a2=14425,b2=8125,e=1+b2a2=1+81144=1512
foci of hyperbola are (±ae,0)i.e(±3,0)
Now given ellipse is x216+y2b2=1
a2=16
Assume eccentricity of this ellipse is e then its foci are (±ae,0)i.e(±4e,0)
Given focci of given hyperbola and ellipse coincide
4e=3e=34
For ellipse, using eccentricity relationship, e2=1b2a2
916=1b216
b2=7

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Hyperbola and Terminologies
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon