Question

Angle made by the lines represented by the equation $xy + y = 0$ with y-axis are
A. ${0^ \circ }\,and\,{90^ \circ }$
B. ${0^ \circ }\,and\,{30^ \circ }$
C. ${30^ \circ }\,and\,{60^ \circ }$
D. ${30^ \circ }\,and\,{90^ \circ }$

Answer 1

Hint: First we will simplify the given equation $xy + y = 0$ so that we can easily find the lines which represent the given equation. After finding the equation of lines we will use the fact that the x-axis is perpendicular to the y-axis and the line $x + a = 0$ is parallel to the y-axis to find the required angles.

Formula Used:
The equation $x + a = 0$ is parallel to the y-axis.
The equation $y = 0$ represents the x-axis.

Complete step by step solution: The given equation is
$xy + y = 0$
We can rewrite the given equation as
$y(x + 1) = 0$
$y=0$, $x+1=0$
Which gives two lines
$x + 1 = 0$ and $y = 0$
Therefore, the line $xy + y = 0$ represents two lines $x + 1 = 0$ and $y = 0$
Now, the line $x + 1 = 0$ is equation of the line which is parallel to y axis
So, it will make an angle of ${0^ \circ }$ with y-axis
Now, the line $y = 0$ is the equation of the x-axis
We know that the x-axis is perpendicular to y-axis
So, it will make an angle of ${90^ \circ }$ with y-axis

Hence, option A is correct.

Additional Information: We know that $x + a = 0$ is the equation of the line which is parallel to the y-axis.So, it will make an angle of ${0^ \circ }$ with the y-axis. And the line $y = 0$ is the equation of the x-axis.We know that the x-axis is perpendicular to the y-axis. So, it will make an angle of ${90^ \circ }$ with the y-axis .

Note: Students should know about the concept of lines which are parallel to y-axis and which are perpendicular to y-axis so that they can get the correct solution.