If `theta` is the measure of acute angle between the pair of line repseented by `ax^(2) + 2hxy + by^(2) = 0` , then prove that
`tan theta = |(2sqrt(h^(2) - ab))/(a+b)|,a + b ne 0 `
Hence find the acture angle between the lines `x^(2) - 4xy + y^(2) = 0`

Explanation

Refer to HSC Paper , Marcj 2017, Answer 2 (B) (ii).
On comparing `x^(2) - 4xy + y^(2) =0` with `ax^(2) + 2hxy + by^(2) = 0`, we get
a = 1 , 2h = - 4 i.e., h = - 2 and b = 1
Let `theta` be the acute angle between the lines.
`therefore " "tan theta = |(2sqrt(h^(2) - ab))/(a+b)|`
` = |(2sqrt((-2)^(2)-1(1)))/(1+1)|`
`=|(2sqrt4-1)/(2)| = sqrt(3)`