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

The range of values of a such that the angle θ between the pair of tangents drawn from (a,0) to the circle x2+y2=1 satisfies π2<θ<π, lies in

A
(1,0)(2,5)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(1,0)(1,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(2,1)(0,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(2,1)(1,2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D (2,1)(1,2)
Given equation of circle is x2+y2=1
C(0,0) and r=1
Angle between pair of tangents is given by
θ=2tan1(rS1)
S1=a2+021
S1=a21 (1)
For (1) to be defined,
a210
(a+1)(a1)0
a(,1][1,) (2)

Now, θ=2tan11a21
Since π2<θ<π,
π2<2tan11a21<π1
π4<tan11a21<π2
1<1a21<
0<a21<1
0<a21<1
a22<0 and a21>0
(a+2)(a2)<0 and (a+1)(a1)>0
a(2,2) and a(,1)(1,)
a(2,1)(1,2) (3)
On taking intersection of (2) and (3), we get
a(2,1)(1,2)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon