Geo3.12

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If the pair of line ax^{2}+2pxy-ay^{2}=0,bx^{2}+2qxy-by^{2}=0\, are such that each pair bisects the angle between the other pair,then show that ab+pq=0\,


Equation to the pair of angle bisectors of ax^{2}+2pxy-ay^{2}=0\,

{\frac  {x^{2}-y^{2}}{a+a}}={\frac  {xy}{p}}\,

px^{2}-2axy-py^{2}=0\,

But the angle bisectors are bx^{2}+2qxy-by^{2}=0\,

{\frac  {p}{b}}={\frac  {-2a}{2q}}={\frac  {-p}{-b}}\,

pq=-ab\,

pq+ab=0\,


Main Page:Geometry:Straight Lines-II