The angle represented by 3x² + 7xy + 2y²= 0 is?
- 30°
- 45°
- 60°
- None of these
Explanation
Equation 3x² + 7xy + 2y² = 0 represents a pair of lines through origin.
Factor it:
3x² + 6xy + xy + 2y² = 0
3x(x + 2y) + y(x + 2y) = 0
(3x + y)(x + 2y) = 0
So lines are: y = -3x and y = -x/2
Slopes: m₁ = -3, m₂ = -1/2
Angle between lines:
tan θ = |(m₁ - m₂)/(1 + m₁m₂)|
= |(-3 + 1/2) / (1 + 3/2)|
= |(-5/2) / (5/2)| = | -1 | = 1
tan θ = 1 → θ = 45°
So the acute angle between the two lines is 45°.
Last verified on 05-06-2026
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