Question

If the lines represented by the equations y + (2p + 1)x + 3 = 0 and 8y − (2p − l)x = 5 are perpendicular to each other, find p.

Answer 1

Given,

⇒ y + (2p + 1)x + 3 = 0

⇒ y = −(2p + 1)x − 3

Comparing above equation with y = mx + c, we get:

⇒ Slope (m₁) = −(2p + 1)

Given,

⇒ 8y − (2p − 1)x = 5

⇒ 8y = (2p − 1)x + 5

⇒ y = `(2p − 1)/8 .  x + 5/8`

Comparing above equation with y = mx + c, we get:

⇒ Slope (m₂) = `(2p − 1)/8`

We know that,

Product of slopes of perpendicular lines = −1

⇒ `−(2p+1) × (2p − 1)/8 = −1`

⇒ `((2p)^2−1^2)/8 = 1`

⇒ 4p² − 1 = 8

⇒  4p² = 9

⇒ `p^2 = 9/4`

⇒ `p = sqrt(9/4)`

⇒ p = `±3/2`

Hence, p = `±3/2​`