Question

Find the length of the tangent from (1, 2) to the circle x² + y² – 2x + 4y + 9 = 0.

Answer 1

The length of the tangent from (x₁, y₁) to the circle x² + y² – 2x + 4y + 9 = 0 is  `sqrt(x_1^2 + y_1^2 - 2x_1 + 4y_1 + 9)`

Length of the tangent from (1, 2) = `sqrt(1^2 + 2^2 - 2(1) + 4(2) + 9)`

`= sqrt(1 + 4 - 2 + 8 + 9)`

`= sqrt20`

`= sqrt(4 xx 5)`

`= 2sqrt5` units