no of circles touching all the lines x-2y+1=0,2x+y+3=0 and 4x-8y+3=0 is

Dear Student,
Please find below the solution to the asked query:

Slope=m=-Coefficient of xCoeffient of y L1: x-2y+1=0m1=-1-2=12L2: 2x+y+3=0m2=-21=-2L3: 4x-8y+3=0m3=-4-8=12As m1=m3Hence L1 and L3  are parallel.As m1×m2=m3×m2=-1Hence m1 and m3 will be perpendicular to m2.Hence arrangement of lines will be like given below.

Hence there will be two common circles touching all 3 lines.Cirlces will be enclosed between two parallel lines.

Hope this information will clear your doubts about this topic.

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