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If $l, m, n$ are in arithmetic progression, then the straight line $l x+m y+n=0$ will pass through the point
Options:
Solution:
1119 Upvotes
Verified Answer
The correct answer is:
$(1,-2)$
Since, $l, m, n$ are in AP.
$$
\therefore \quad 2 m=l+n
$$
Given equation of line is
$$
l x+m y+n=0
$$
Now, assume that the point $(1,-2)$ satisfy the given equation.
$$
\begin{array}{lrr}
\therefore & l-2 m+n=0 \\
\Rightarrow & 2 m=l+n \\
\Rightarrow & l, m, n \text { are in AP. }
\end{array}
$$
Hence, option (2) is correct.
$$
\therefore \quad 2 m=l+n
$$
Given equation of line is
$$
l x+m y+n=0
$$
Now, assume that the point $(1,-2)$ satisfy the given equation.
$$
\begin{array}{lrr}
\therefore & l-2 m+n=0 \\
\Rightarrow & 2 m=l+n \\
\Rightarrow & l, m, n \text { are in AP. }
\end{array}
$$
Hence, option (2) is correct.
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