CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the equation of the hyperbola whose vertices are (0, ±3) and the foci are (0, ±5).

Open in App
Solution

Since the vertices of the given hyperbola are of the form (0, ±a), it is a vertical hyperbola.

Let the required equation be y2a2x2b2=1.

Then, its vertices are (0, ±a).

But, it is given that the vertices are (0, ±3).

a=3.

Let its foci be (0, ±c).

But, it is given that the foci are (0, ±5).

c=5.

Now, b2=(c2a2)=(5232)=(259)=16.

Thus, a2=32=9 and b2=16.

Hence, the required equation is y29x216=1.


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