Question

If the straight lines 12y = − (p + 3)x + 12, 12x – 7y = 16 are perpendicular then find ‘p’

Answer 1

Slope of the first line 12y = − (p + 3)x + 12

y = `(-("p" + 3)x)/12` + 1   ...(Comparing with y = mx + c)

Slope of the second line (m₁) = `(-("p" + 3))/12`

Slope of the second line 12x – 7y = 16

(m₂) = `(-"a")/"b" = (-12)/(-7) =12/7`

Since the two lines are perpendicular

m₁ × m₂ = − 1

`(-("p" + 3))/12 xx 12/7` = − 1

⇒ `(-("p" + 3))/7` = − 1

− (p + 3) = − 7

– p – 3 = − 7

⇒ − p = − 7 + 3
− p = − 4

⇒ p = 4

The value of p = 4