Question

# Let $$a,b,c$$ are in A.P. then the line $$ax+by+c=0$$ always passes through which fixed point

A
(1,2)
B
(1,2)
C
(1,2)
D
(1,2)

Solution

## The correct option is A $$(1,-2)$$Given, $$a,b,c$$ are in A.P. .Then $$b-a=c-b$$or, $$c=2b-a$$......(1).Now the equation of the line $$ax+by+c=0$$ can be written as,$$ax+by+(2b-a)=0$$ [ Using (1)]or, $$a(x-1)+b(y+2)=0$$This is true for all $$a,b$$ then $$x-1=0$$ and $$y+2=0$$ or, $$x=1,y=-2$$.So the fixed point is $$(1,-2)$$.Mathematics

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