Question

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.

विकल्प

• `tan^-1 (5/3)`

• `2tan^-1 (1/3)`

• `2tan^-1 (3/2)`

• `2tan^-1 (2/3)`

Answer 1

`2tan^-1 (3/2)`

Explanation:

x² + y² = 9²

∴ r = 3 unit

Now point (1, 2) is translated 2 units through the positive

Direction of x-axis

So New point (3, 2)

∴ Distance between P' and O is

P'O = `sqrt((3 - 0)^2 + (2 - 0)^2) = sqrt(13)` 

∴ P'A² + AO² = P'O²

⇒ P'A² = `(sqrt(13))^2 - (3)^2`

P'A = 13 – 9 = 4

P'A = 2 unit

∵ tan θ = `3/2`

∴ θ = `tan^-1 (3/2)`

Now angle AP'B = 2 × θ = `2tan^-1 (3/2)`