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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 ba=cb
or, c=2ba......(1).
Now the equation of the line ax+by+c=0 can be written as,
ax+by+(2ba)=0 [ Using (1)]
or, a(x1)+b(y+2)=0
This is true for all a,b then x1=0 and y+2=0 or, x=1,y=2.
So the fixed point is (1,2).

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