The angle between pair of lines whose equation is 4xsquare +10 xy +m y square + 5x +10 y = 0 is answer shows tan inverse 3/8, is it correct if not what is its answer.
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4 x^2 + 10 x y + m y^2 + 5 x + 10 y = 0y^2 + 10/m xy + 4/m x^2 + 5/m x + 10/m y = 0
As the constant term is 0, the constant term in one of the Lines is also 0.(y - m1 x) (y - m2 x - c) = 0y^2 - (m1 + m2) xy + m1 m2 x^2 + c m1 x - c y = 0m1 + m2 = -10/m m1 m2 = 4/m c m1 = 5/m c = -10/mm1 = -1/2=> m2 = -8/m = -10/m +1/2=> 2/m = 1/2 => m = 4 => m2 = -2
angle = tan^-1 |(2 -1/2) /(1 +2*1/2) | = tan^-1 3/4
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we can also apply the condition on the coefficients of the equation of the pair of lines, to evaluate "m" first, and then find the angle between the two lines. Can use the formula for that.
As the constant term is 0, the constant term in one of the Lines is also 0.(y - m1 x) (y - m2 x - c) = 0y^2 - (m1 + m2) xy + m1 m2 x^2 + c m1 x - c y = 0m1 + m2 = -10/m m1 m2 = 4/m c m1 = 5/m c = -10/mm1 = -1/2=> m2 = -8/m = -10/m +1/2=> 2/m = 1/2 => m = 4 => m2 = -2
angle = tan^-1 |(2 -1/2) /(1 +2*1/2) | = tan^-1 3/4
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we can also apply the condition on the coefficients of the equation of the pair of lines, to evaluate "m" first, and then find the angle between the two lines. Can use the formula for that.
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