If $a,\ b,\ c$ are in A.P., then find the point from which straight lines $ax+by+c=0$ wil always pass through.
Given: $a,\ b,\ c$ are in A.P.
To do: To find the point from which straight lines $ax+by+c=0$ wil always pass through.
Solution:
If $a,\ b,\ c$ are in A.P then
$a + c = 2 b$
$\Rightarrow a − 2 b + c = 0$
On comparing it to $ax + by + c = 0$, $x=1,\ y=-2$
Thus, it passes through $( 1,\ − 2)$
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