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Question: If q is the angle between the tangents drawn from (1, –1) to the circle (x + 2)<sup>2</sup> + (y – 1...

If q is the angle between the tangents drawn from (1, –1) to the circle (x + 2)2 + (y – 1)2 = 9 then sin q =

A

5/13

B

7/13

C

12/13

D

1

Answer

12/13

Explanation

Solution

q = 2 tan–1 (rS1)\left( \frac{r}{{\sqrt{S}}_{1}} \right) ̃ q = 2 tan1(39+4−9)\left( \frac{3}{\sqrt{9 + 4 - 9}} \right)

θ2\frac{\theta}{2}=tan–1(32)\left( \frac{3}{2} \right)̃ tanθ2\frac{\theta}{2}=32\frac{3}{2}

̃ sin2.θ2=2tan⁡θ/21+tan⁡2θ/2\frac{\theta}{2} = \frac{2\tan\theta/2}{1 + \tan^{2}\theta/2}

sin q = 2×3/21+9/4=1213\frac{2 \times 3/2}{1 + 9/4} = \frac{12}{13}