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

The equation x212k + y28k = 1 represents.


A

A hyperbola, if

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

A ellipse, if

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

A hyperbola, if

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

None of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

A hyperbola, if


You try to imagine first the standard forms of hyperbola and ellipse.

Hyperbola x2a2 y2b2=1 or y2b2 x2a2=1

Ellipse x2a2 y2b2=1

This shows that for the curve to become a hyperbola the

coefficients should be of opposite signs.

Applying this condition for the given curve.

(12k)(8k) < 0

i.e., (12k)(k8) < 0

If the given curve is an ellipse the coefficients of x2 and y2 should

be positive sign.For the curve to be an ellipse.

i.e.,12k < 0 and 8k < 0

i.e.,k < 12 and k < 0

Hence option (c)


flag
Suggest Corrections
thumbs-up
6
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Jumping to Details
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon