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


1