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