Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If a tangent having slope of -4/3 to the ellipse 
intersects the major and minor axes in points A and B respectively, then the area of the Δ Δ OAB is equal to
Text Solution
Verified by ExpertsThe correct answer is:
D
Let P (x 1 , y 1 ) be a point on the ellipse 
.
Then 
The equation of the tangent at (x 1 , y 1 ) is 
This meets the axes at A 
and B 
It is given that the slope of the tangent at (x 1 , y 1 ) is -3/4, therefore,
⇒ ⇒ 
(say)
⇒ ⇒ x 1 = 3k, y 1 = 4k
Putting x 1 , y 1 in (1), we get, k 2 = 1
Now, area of Δ Δ OAB = 
. OA.OB = 
. 
= 
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