Geo3.14

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Prove that the pair of lines (a-\lambda )x^{2}+2hxy+(b-\lambda )y^{2}=0\, is equally inclined with the pair ax^{2}+2hxy+by^{2}=0\,

Equation to the pair of angle of bisectors of (a-\lambda )x^{2}+2hxy+(b-\lambda )y^{2}=0\, is

{\frac  {x^{2}-y^{2}}{(a-\lambda )-(b-\lambda )}}={\frac  {xy}{h}}\,

{\frac  {x^{2}-y^{2}}{a-b}}={\frac  {xy}{h}}\,

which is also the equation tot he angle bisectors of ax^{2}+2hxy+by^{2}=0\,

Hence the given two pairs of lines are equally inclined.


Main Page:Geometry:Straight Lines-II