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

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