Find the angles between each of the following pairs of straight lines :

(m² – mn) y = (mn + n²)x + n³ and (mn + m²)y = (mn – n²)x + m³.

Given:

The equations of the lines are

(m² − mn) y = (mn + n²) x + n³ … (1)

(mn + m²) y = (mn − n²) x + m³ … (2)

To find:

Angles between two lines.

Explanation:

Let m₁ and m₂ be the slopes of these lines.

∴

Let θ be the angle between the lines.

Then,

⇒

⇒

Then,

⇒

⇒

Hence, the acute angle between the lines is