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Question
Find the measure of the acute angle between the line represented by:
2x2 + 7xy + 3y2 = 0
Solution
Comparing the equation
2x2 + 7xy + 3y2 = 0 with
ax2 + 2hxy + by2 = 0, we get,
a = 2, 2h = 7 i.e. h = `7/2` and b = 3
Let θ be the acute angle between the lines.
∴ tan θ = `|(2 sqrt("h"^2 - "ab"))/("a + b")|`
= `|(2 sqrt((7/2)^2 - 2(3)))/(2 + 3)|`
= `|(2 sqrt((49/4) - 6))/(5)|`
= `|(2 sqrt(((49 - 24)/4)))/(5)|`
= `|(2 sqrt((25/4)))/(5)|`
= `(2 xx (5/2))/5`
= `5/5`
tan θ = 1
∴ θ = tan 1 = 45°
∴ θ = 45°
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