Question

Find the acute angle between the lines represented by xy + y² = 0.

Answer 1

Comparing the equation xy + y² = 0 with ax² + 2hxy + by² = 0, we get

a = 0, 2h = 1, i.e., h = `1/2` and b = 1

Let θ be the acute angle between the lines

∴ tan θ = `|(2sqrt(h^2 - ab))/(a + b)|`

= `|(2sqrt((1/2)^2 - 0(1)))/(1 + 1)|`

= `|(2sqrt(1/4 - 0))/1|`

= `|2 xx 1/2|`

= 1

∴ tan θ = `tan  pi/4`

∴ θ = `pi/4`