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Question

Let the algebraic sum of the perpendicular distance from the points (2,0)(0,2) and (1,1) to a variable straigth line be zero, then the passes through a fixed point whose coordinates are........ Find the condition on a and b, such that the portion of thelineax+by1=0, intercepted between the line axis.

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Solution

variable0fax+by+c=0

algebricsumofperpendicular(20)(02)(11)

[2×a+b×0+ca2+b2]+[a×0+b×2+ca2+b2]+[a×1+b×1+ca2+b2]

±(2a+ca2+b2)±(2b+ca2+b2)±(a+b+ca2+b2)

2a+c+2b+c+a+b+c=0

3a+3b+3c=0

a+b+c=0



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