Find the acute angle between the lines represented by 3x2 + 2xy - y2 = 0
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Given : the lines represented by 3x² + 2xy - y² = 0
To Find : acute angle between the lines
Solution:
3x² + 2xy - y² = 0
=> 3x² + 3xy - xy - y² = 0
=> 3x(x + y) - y(x + y) = 0
=> (3x - y)(x + y) = 0
=> 3x - y = 0 and x + y = 0
3x - y = 0
=> y = 3x
slope = 3
x + y = 0
=> y = -x
slope = -1
α acute angles between lines
Tanα = | (3 - (-1) ) /( 1 + 3(-1)) |
=> Tanα = | 4) /(-2 ) |
=> Tanα = 2
=> α = Tan⁻¹2
α = 63.435°
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