Question

Lines mx + 3y = −7 and 5x − ny = 3 are perpendicular to each other. Find the relation connecting m and n.

Answer 1

Given lines,

⇒ mx + 3y = −7 and 5x − ny = 3

⇒ 3y = mx + 7 and ny = 5x − 3

⇒ y = `m/3x + 7/3​ and y = 5/nx − 3/n`

Comparing above equations with y = mx + c we get,

Slope of 1st line = `m/3`

Slope of 2nd line = `5/n`

Since, product of slopes of perpendicular lines = −1

∴ `m/3 × 5/n =−1`

⇒ `(5m)/(3n) = −1`

⇒ 5m = −3n

⇒ 5m + 3n = 0