Question

If the line 3x + 4y = m touches the circle x² + y² = 10x, then m is equal to ______.

Options

• –40, 10

• 40, –10

• 40, 10

• –40, –10

Answer 1

If the line 3x + 4y = m touches the circle x² + y² = 10x, then m is equal to 40, –10.

Explanation:

∴ Perpendicular drawn from its centre = its radius

Radius of circle = `sqrt((5)^2` = 5

Length of ⊥^r = `|15 + 0 - m|/sqrt(9 + 16)` = 5

⇒ |15 – m| = 25

⇒ 15 – m = ±25

⇒ m = –10, 40