Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If α , β are the eccentric angles of the extremities of a focal chord of the ellipse x 2 /16 + y 2 /9 = 1, then tan ( α /2) tan ( β /2) =
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
D
The equation of the ellipse is of the form
x 2 /a 2 + y 2 /b 2 = 1 where a 2 = 16, b 2 = 9
∴ the eccentricity e = 
= 
.
Let P(4 cos α , 3 sin α ) and Q (4 cos β , 3 sin β ) be a focal chord of the ellipse passing through the focus at ( 
, 0).
Then 
= 
⇒ 
= 
⇒ 
= 
⇒ tan 
tan 
= 
= 
.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is
If distance between the directrices be thrice the distance between the foci, then eccentricity of e…
The equation of the ellipse whose centre is at origin and which passes through the points (–3, 1) a…
If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus re…
If the foci and vertices of an ellipse be and , then the minor axis of the ellipse is
The equations of the directrices of the ellipse are