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Question
Find the measure of the acute angle between the line represented by `3"x"^2 - 4sqrt3"xy" + 3"y"^2 = 0`
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Solution
Given equation of the lines is `3"x"^2 - 4sqrt3"xy" + 3"y"^2 = 0`
Comparing with ax2 + 2hxy + by2 = 0,
We get, a = 3, h = `-2 sqrt3` and b = 3
Let θ be the acute angle between the lines.
∴ tan θ = `|(2 sqrt("h"^2 - "ab"))/("a + b")|`
= `|(2 sqrt((- 2 sqrt3)^2 - 3(3)))/(3 + 3)|`
= `|(2sqrt(12-9))/6|`
= `|sqrt(3)/3|`
∴ tan θ = `1/sqrt3`
= θ = `tan^-1(1/sqrt(3))`
∴ θ = 30°
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