First slide

Definition of a circle

Question

The range of values of a such that the angle $θ$ between the pair of tangents drawn from $(a, 0)$ to the circle $x^{2} + y^{2} = 1$ lies in the interval $(\frac{π}{3}, π)$ is

Moderate

A

$(- 2, - 1) \cup (1, 2)$
B

$(- 2, 0) \cup (0, 1)$
C

$(- 2, 2)$
D

$(- 2, 0) \cup (0, 2)$

Solution

$\tan \frac{θ}{2} = \frac{1}{\sqrt{a^{2} - 1}}$
$\Rightarrow \frac{1}{\sqrt{3}} < \frac{1}{\sqrt{a^{2} - 1}} < \infty$
$\Rightarrow a^{2} - 1 < 3$ and $a^{2} - 1 > 0$

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