Geo3.13

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Prove that one of the lines ax^{2}+2hxy+by^{2}=0\, will bisect the angle between the coordinate axes if (a+b)^{2}=4h^{2}\,

Equation to the pair of axes is xy=0\,

Equation to the bisectors of the angle between the axes are x^{2}-y^{2}=0,y=\pm x\,

This line belongs to ax^{2}+2hxy+by^{2}=0\,

ax^{2}+2hx(\pm x)+bx^{2}=0\,

(a+b)=\pm 2h\,

Squaring on both sides, we get

(a+b)^{2}=4h^{2}\,


Main Page:Geometry:Straight Lines-II