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Question
Find the measure of the acute angle between the lines given by x2 − 4xy + y2 = 0
Solution
Given equation of the lines is x2 – 4xy + y2 = 0
Comparing with ax2 + 2hxy + by2 = 0
We get a = 1, h = – 2, b = 1
Let θ be the acute angle between the lines.
∴ `tanθ = |(2sqrt("h"^2 - "ab"))/("a" + "b")|`
= `|(2sqrt((-2)^2 - (1)(1)))/(1 + 1)|`
= `|(2sqrt(4 - 1))/(1 + 1)|`
`=|sqrt(3)|`
∴ tan θ = `sqrt(3)`
∴ θ = `tan^-1(sqrt(3))`
∴ θ = 60°
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