Question

If the line y = `sqrt(3)x + k` touches the circle x² + y² = 16, then find the value of k.

Answer 1

Given circle is x² + y² = 16

Centre = (0, 0)

Perpendicular from the origin to the given line y = `sqrt(3)x + k` is equal to the radius.

∴ 4 = `|(0 - 0 - k)/sqrt((1)^2 + (sqrt(3))^2)|`

= `|(-k)/sqrt(4)|`

⇒ 4 = `+- k/2`

⇒ k = `+-  8`.

Hence, the required values of k are ± 8.