Question

what is the point through which ax+by+c=0 should pass such that a,b,c are in A.P?

Answer 1

a x + b y + c = 0

b = (a  + c) /2

2 a x + (a +c) y + 2 c = 0
a (2 x + y ) + c (y + 2) = 0

So if  2 x + y = 0  and  y + 2 = 0    then,  a , b, c are always in Arithmetic Progression irrespective of their values.

so the  point is :  y = -2,  and x = 1  ie.,  (1, -2).

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verify:       substitute the values of x and y:
           a * 1 - 2 * b + c = 0