If a+2b+3c = 0 then a/3+2b/3+c = 0 and comparing with line ax+ by +v, we - Maths - Straight Lines

Question

​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

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

Shivam Mishra · Accepted Answer

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

Hope this information will clear your doubts about this topic

If you have any doubts just ask here on the ask and answer forum
and our experts will try to help you out as soon as possible
Regards