wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Tangent is drawn to ellipse x227+y2=1 at
(33cosθ,sinθ) (where,θ(0,π2)).
Then, the value of θ such that the sum of intercepts on axes made by this tangent is minimum, is


A

π3

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

π6

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

π8

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

π4

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

The correct option is B

π6


Given, tangent is drawn at (33cosθ,sinθ) to x227+y21=1.
Equation of tangent is xcosθ33+ysinθ1=1.
Thus, sum of intercepts =(33cosθ+1sinθ)=f(θ) [say]
f(θ)=33sin3θcos3θsin2θcos2θ, put f(θ)=0
sin3θ=133/2cos3θ
tanθ=13,i.e.θ=π6 and at θ=π6,f′′(0)>0
Hence, tangent is minimum at θ=π6.


flag
Suggest Corrections
thumbs-up
15
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Line and Ellipse
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon