If  a+2b+3c = 0  then  a/3+2b/3+c = 0 and comparing with  line ax+ by +v, we get  x = 1/3 & y = 2/3 so there will be a point (1/3, 2/3) from where  each  of the  lines of the form ax + by +c = 0 will pass for the  given  relation between  a. b. c. we can say  if there  exists a linear relation  between  a.b.c then the family of straight  lines of the form of ax + by +c pass  through  a fixed point.
  1. If a,b ,c are in HP, then  the line acx +bcy +ab = 0 passes through ?

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

We haveacx+bcy+ab=0...iAs a,b,c are in H.P., henceb=2aca+cab+bc=2ac-2ac+bc+ab=0...iiOn comparing i and ii, we getx=-2 and y=1Hence line acx+bcy+ab=0 passes through -2,1

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