​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 distinct  real numbers and a2+b2+c2 = 3abc , then  the line ax + by +c = 0 passes through ?

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

I think it should be a3+b3+c3=3abc, not a2+b2+c2=3abcNow we haveax+by+c=0....iWe know that:a3+b3+c3=3abc whena+b+c=0...iiComparing i and ii, we getx=1 and y=1Hence line always passes through 1,1.

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