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

If z=3(2+cosθ+isinθ), then locus of z is

A
a straight line
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a circle having center on the y-axis
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a parabola
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a circle having center on the x-axis
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D a circle having center on the x-axis
z=3(cosθ+2)+i(sinθ)
=3[(cosθ+2)isinθ](cosθ+2)2+sin2θ
=3(cosθ+2)isinθ5+4cosθ
=35+4cosθ((cosθ+2)isinθ)
=a(cosθ+2)isinθ)
Now
x=a(cosθ+2)
xa2=cosθ
And y=asinθ
ya=sinθ
Hence (xa2)2+y2a2
=1
(x22a)2+y2=a2
Hence it is a circle, centered at (2a,0) where a=35+4cosθ

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Area under the Curve
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon