Geo3.11

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Find the equation to the pair of angle bisectorsof the pair of lines (ax+by)^{2}=3(bx-ay)^{2}\,

Simplifying the given pair, we have x^{2}(a^{2}-3b^{2})+8abxy+y^{2}(b^{2}-3a^{2})=0\,

Therefore,equation to the pair of bisectors of angles between them is {\frac  {x^{2}-y^{2}}{(a^{2}-3b^{2})-(b^{2}-3a^{2})}}={\frac  {xy}{4ab}}\,

ab(x^{2}-y^{2})=(a^{2}-b^{2})xy\,

(ax+by)(bx-ay)=0\,

Therefore,equations to the bisectors are ax+by=0,bx-ay=0\,


Main Page:Geometry:Straight Lines-II