Geo3.5

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Find the equation to the two lines represented by the equation x^{2}-2xy\csc \theta +y^{2}=0\,

Given x^{2}-2xy\csc \theta +y^{2}=0\,

x={\frac  {-2y\csc \theta \pm {\sqrt  {4y^{2}\csc ^{2}\theta -4y^{2}}}}{2}}={\frac  {1}{2}}[-2y\csc \theta \pm 2y{\sqrt  {\csc ^{2}\theta -1}}]\,


x=-y\csc \theta \pm y\cot \theta \,

x=-y(\csc \theta \pm \cot \theta )\,

Therefore the two lines are x+y(\csc \theta +\cot \theta )=0,x+y(\csc \theta -\cot \theta )=0\,


Main Page:Geometry:Straight Lines-II