Find the measure of acute angle between the lines represented by 2x² + 7xy + 3y² = 0
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The given equation is 2x2 – 7xy + 3y2 = 0.
This can be written as 2x2 – 7xy + 3y2 = (2x – y)(x-3y)
Therefore, the given lines are (2x – y) = 0 and (x-3y) = 0.
Now, here, a = 2, h = 7/2 and b = 3.
Hence, the angle between the lines is given by tan θ = 2√{(7/2)2 – 6}/5 = 1.
Hence, θ = 45°.
This can be written as 2x2 – 7xy + 3y2 = (2x – y)(x-3y)
Therefore, the given lines are (2x – y) = 0 and (x-3y) = 0.
Now, here, a = 2, h = 7/2 and b = 3.
Hence, the angle between the lines is given by tan θ = 2√{(7/2)2 – 6}/5 = 1.
Hence, θ = 45°.
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