If a point (1, 2) is translated 2 units through the positive direction of x-axis and then the tangents drawn from that point to the circle x² +y² = 9, find the angle between the tangents.

Correct option is C

Given:

circle equation =x² +y² = 9

a point (1, 2) is translated 2 units through the positive direction of x-axis

Solution:

$$x^2+y^2 =a^2$$

so radius = 3 unit

point 1,2 is moves by 2 unit 

distance between p' and  o=

​$$P'O = \sqrt{(3 - 0)^2 + (2 - 0)^2} = \sqrt{13}$$ 

$$P'A^2 + AO^2 = P'O^2$$ 

$$P'A^2 = (\sqrt{13})^2 - (3)^2$$ 

$$P'A = 2 \text{ unit}$$ 

$$\tan \theta = \frac{3}{2}$$ 

$$\theta = \tan^{-1} \left(\frac{3}{2}\right)$$ 

$$\text{Angle AP'B} = 2 \times \theta = 2 \tan^{-1} \left(\frac{3}{2}\right)$$​​
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