Question

Find the value of p if the lines, whose equations are 2x – y + 5 = 0 and px + 3y = 4 are perpendicular to each other.

Answer 1

2x − y + 5 = 0

y = 2x + 5

Slope of this line = 2

px + 3y = 4

3y = − px + 4

`y = (-px)/3+ 4/3`

Slope of this line = `(-p)/3`

Since, the lines are perpendicular to each other, the product of the slopes is −1.

∴ `(2)((-p)/3)= -1`

`(2p)/3 = 1`

`p = 3/2`