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 in HP, then the line acx +bcy +ab = 0 passes
through ?

Shivam Mishra · Accepted Answer

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+c⇒ab+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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