Question

Find the value, of k, if the line represented by kx – 5y + 4 = 0 and 4x – 2y + 5 = 0 are perpendicular to each other.

Answer 1

Here, kx - 5y + 4 = 0
⇒ y = `(kx)/(5) + (4)/(5)`
∴ The slope of the line is `k/(5)`.
Also 4x - 2y + 5 = 0
y = `2x + (5)/(2)`
∴ The slope of line is 2.
Since, the given lines are perpendicular to each other, we have
`(k/5)(2)` = -1
⇒ k = `(-5)/(2)`.