Geo3.18

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Find the equation to the pair of bisectors of angles between 3x^{2}+4xy-4y^{2}-11x+2y+6=0\,

From the given equation a=3,b=-4,c=6,h=2,g={\frac  {-11}{2}},f=1\,

The point of intersection is \left({\frac  {(2(1)+4({\frac  {-11}{2}})}{3(-4)-4}},{\frac  {{\frac  {-11}{2}}(2)-3(1)}{-12-4}}\right)\,

({\frac  {5}{4}},{\frac  {7}{8}})\,

Now the pair of lines thro'the origin and parallel to the given pair is 3x^{2}+4xy-4y^{2}=0\,

Therefore,the equation to the pair of angle bisectors is {\frac  {x^{2}-y^{2}}{3+4}}={\frac  {xy}{2}}\,

2x^{2}-7xy-2y^{2}=0\,

Hence the equation to the pair of angle bisectors of the given pair of line is

2(x-{\frac  {5}{4}})^{2}-7(x-{\frac  {5}{4}})(y-{\frac  {7}{8}})-2(y-{\frac  {7}{8}})^{2}=0\,


Main Page:Geometry:Straight Lines-II