Geo3.2

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Find the equation to the pair of lines through the origin and forming an equilateral triangle with the line x-2y-1=0\,.Find also the area of the triangle.

The pair of lines is (ax+by)^{2}-3(bx-ay)^{2}=0\,

Therefore for the line x-2y-1=0\, the required line is

(x-2y)^{2}-3(2x+y)^{2}=0\,

11x^{2}+16xy-y^{2}=0\,

Area of the triangle is {\frac  {c^{2}}{{\sqrt  {3}}(a^{2}+b^{2})}}={\frac  {(-1)^{2}}{{\sqrt  {3}}(1+(-2)^{2})}}\,

{\frac  {1}{5{\sqrt  {3}}}}\,


Main Page:Geometry:Straight Lines-II