Find the measure of acute angle between the lines given by x2 – 4xy + y2 = 0. - Mathematics and Statistics

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Sum

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

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Solution

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`

Concept: Acute Angle Between the Lines
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