Geo3.3

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Find the condition that the lines represented by ax^{2}+2hxy+by^{2}=0\, are such that the slope of one line is \lambda \, times that of the other.

Let the two lines be y=mx,y=\lambda mx\,

We know that m+\lambda m={\frac  {-2h}{b}},m(\lambda m)={\frac  {a}{b}}\,

m(1+\lambda )={\frac  {-2h}{b}},\lambda m^{2}={\frac  {a}{b}}\,

Eliminating m,we get \lambda [{\frac  {-2h}{b(1+\lambda )}}]^{2}={\frac  {a}{b}}\,

ab(\lambda +1)^{2}=4\lambda h^{2}\,


Main Page:Geometry:Straight Lines-II