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

If the tangent drawn at point (t2,2t) on the parabola y2=4x, is same as the normal drawn at point (5cosθ,2sinθ) on the ellipse 4x2+5y2=20 ,then:

A
θ=cos1(15)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
θ=cos1(15)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
t=25
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
t=±15
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct options are
B θ=cos1(15)
C t=±15
The equation of the tangent at (t2,2t) to the parabola
y2=4x is
2ty=2(x+t2)
ty=x+t2
xty+t2=0 (i)
The equation of the normal at point (5cosθ,2sinθ) on the ellipse 5x2+5y2=20 is
(5secθ)x(2cosecθ)y=54
(5secθ)x(2cosecθ)y=1 (ii)
Given that Eqs. (i) and (ii) represent the same line.
5secθ1=2cosecθt=1t2
t=25cotθ and t=12sinθ
25cotθ=12sinθ
4cosθ=5sin2θ
5cos2θ4cosθ5=0
(cosθ5)(5cosθ+1)=0
cosθ=15[cosθ5]
θ=cos1(15)
Putting cosθ=15 in t=12sinθ, we get
t=12115=±15
Hence, θ=cos1(15) and t=±15.

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