Question

Find the value of k for which the lines kx – 5y + 4 = 0 and 5x – 2y + 5 = 0 are perpendicular to each other.

Answer 1

 kx − 5y + 4 = 0

`=>` 5y = kx + 4

`=> y = k/5 x + 4/5`

Slope of this line = `m_1 = k/5`

5x − 2y + 5 = 0

`=>` 2y = 5x + 5

`=> y = 5/2 x + 5/2`

Slope of this line = `m_2 = 5/2`

Since, the lines are perpendicular, m₁ × m₂ = –1

`=> k/5 xx 5/2 = -1`

`=>` k = –2