wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola x216y29=1

Open in App
Solution

b'
x216y29=1 .......(1)
The above equation is of the form
x2a2y2b2=1 .......(2)
So, axis of hyperbola is xaxis,
Comparing (1) and (2) we have
a2=16a=4 and b2=9b=3
Now, c2=a2+b2=16+9=25
c=25=5
Coordinate of foci=(±c,0)=(±5,0)
Hence co-ordinates of foci are (5,0) and (5,0)
Co-ordinate of vertices=(±a,0)=(±4,0)
So, Co-ordinate of vertices are (4,0) and (4,0)
Eccentricitye=ca=54
latus rectum=2b2a=2×94=92
'

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Defining Conics
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon