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If 4x^2+4xy=0 is a equation of pair of straight line and \tan^{-1}m is is angle between two line then find out the value of m?

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

None of these


Answers (1)

best_answer

 

 

Homogeneous Equations in Two Variables -

Homogeneous Equations in Two Variables

Homogeneous equations are those equations where each term has the same degree.

The equation ax2 + 2hxy + by2 = 0 is a homogeneous equation of second degree, it represents two straight lines through the origin.

  1. The lines are real and distinct if h2 - ab  > 0

  2. The lines are coincident, if h2 - ab = 0

  3. The lines are perpendicular, if a + b = 0

Angle between pair of Straight Lines

General equation of pair of straight line is ax2 + 2hxy + by2 + 2gx + 2fy + c = 0.

  1. Angle between the pair of the straight line is 

\\\mathrm{\theta=\tan^{-1}\left \{ \frac{2\sqrt{h^2-ab}}{|a+b|} \right \}}

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4x^2+4xy=0\\ \begin{array}{l}{\text { Angle between the pair of the straight line is }} \\ {\theta=\tan ^{-1}\left\{\frac{2 \sqrt{h^{2}-a b}}{|a+b|}\right\}}\end{array}\\ a=4,b=0,h=2\\ \theta=\tan ^{-1}\left\{\frac{2 \sqrt{2^{2}-4 \times 0}}{|4+0|}\right\}\\ \theta=\tan ^{-1}(1)\\ m=1

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Kuldeep Maurya

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