Q.

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 lies in the interval (π3,π) is

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a

(−2,−1)∪(1,2)

b

(−2,0)∪(0,1)

c

(−2,2)

d

(−2,0)∪(0,2)

answer is A.

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Detailed Solution

tanθ2=1a2-1 ⇒13<1a2−1<∞⇒a2−1<3 and a2−1>0
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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 lies in the interval (π3,π) is