Question

The line $lx+my+n=0$ will be parallel to the x-axis, if
A. $l=m=0$
B. $m=n=0$
C. $l=n=0$
D. $l=0$

Answer 1

Hint: In this question, we are to find the condition for the given line, so that it becomes parallel to the x-axis. Since we know that the line parallel to the x-axis is $y=k$ where $x=0$, we can able to find the required value.



Formula Used:The standard equation of a line is in the form of $ax+by+c=0$
The line parallel to the x-axis is $y=k$
The line parallel to the y-axis is $x=k$
The equation of the x-axis is $y=0$
The equation of the y-axis is $x=0$



Complete step by step solution:Given line is $lx+my+n=0$
The line parallel to the x-axis is $y=k$ where $x=0$.
So, to make the given line $lx+my+n=0$ to be parallel to the x-axis, substitute $x=0$ in the given equation.
Then,
$\begin{align}
  & lx+my+n=0;x=0 \\
 & \Rightarrow l(0)+my+n=0 \\
 & \Rightarrow my+n=0 \\
 & \Rightarrow y=-n/m \\
\end{align}$
Since the obtained equation is in the form of $y=k$, the given line is parallel to the x-axis.
Thus, the given line is parallel to the x-axis if the coefficient of $x$ is zero. I.e., $l=0$.



Option ‘D’ is correct



Note: Here we need to remember that for a line to be parallel to the x-axis, it must be in the form of $y=k$. So, for writing an equation with $x$ and $y$ variables with only one variable, the other variable’s coefficient must be put to zero. Thus, we get the required equation which is parallel to the x-axis.