Question

find the acute angle between the lines
x² – 4xy + y² = 0.

Answer 1

The given pair of lines are x² – 4xy + y² = 0
Comparing with ax² + 2hxy + by² = 0, we get

a = 1, h = –2, b = 1

`tantheta=|(2sqrt(h^2-ab))/(a+b)|=|(2sqrt(4-1))/(1+1)|`

`=|(2sqrt3)/2|`

`tantheta=sqrt3`

`theta=60^@ or pi/3`