Geo4.22

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Show that the lines 2x-5y+1=0,6y-15x+2=0\, intersect the coordinate axes in concyclic points. Also find the equation of the circle passing through those points.

Given lines are

2x-5y+1=0,15x-6y-2=0\,

The codition for two lines intersect the coordinate axes is

a_{1}a_{2}=b_{1}b_{2}\,

2(15)=(-5)(-6)\,

Hence the lines cut the axes in concyclic points.

Now the equation of the circle through these points is

(2x-5y+1)(15x-6y-2)-[2(-6)-5(15)]xy=0\,

30x^{2}-12xy-4x+30y^{2}-75xy+10y+15x-6y-2+87xy=0\,

30x^{2}+30y^{2}+11x+4y-2=0\,


Main Page:Geometry:Circles