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Show that the lines 2x+3y-12=0 and 3x+2y-2=0 are conjugate lines with respect to the circle x^{2}+y^{2}=2\,

Given circle is x^{2}+y^{2}=2\, and the lines are 2x+3y-12=0,3x+2y-2=0\,

Now according to the condition


In the above equations, r^{2}=2,l_{1}=2,l_{2}=3,m_{1}=3,m_{2}=2,n_{1}=-12,n_{2}=-2\,

2(2\cdot 3+3\cdot 2)=(-12)(-2)\,


Since the condition is satisfied, the two lines are conjugate with respect to the given circle.

Main Page:Geometry:Circles