We will learn how to find the equation of y-axis and equation of a line parallel to y-axis.
Let AB be a straight line parallel to y-axis at a distance a units from it. Then, clearly, all points on the line AB have the same abscissa a. Thus, AB can be considered as the locus of a point at a distance a from y-axis and all points on the line AB satisfy the condition x = a.
Thus, if P(x, y) is any point on AB, then x = a.
Hence, the equation of a straight line parallel to y-axis at
a distance a from it is x = a.
The equation of y-axis is x = 0, since, y-axis is a parallel to itself at a distance 0 from it.
Or
Let P (x, y) be any point on the y-axis. Then clearly, for all position of P we shall the same abscissa 0 or, x = 0.
Therefore, the equation of y-axis is x = 0.
If a straight line is parallel and to the left of x-axis at a distance a, then its equation is x = -a.
Solved examples to find the equation of y-axis and equation of a line parallel to y-axis:
1. Find the equation of a straight line parallel to y-axis at a distance of 3 units on the left hand side of y-axis.
Solution:
We know that the equation of a straight line is parallel and to the left of x-axis at a distance a, then its equation is x = -a.
Therefore, the equation of a straight line parallel to y-axis at a distance of 3 units on the left hand side of y-axis is x = -3
2. Find the equation of a straight line parallel to y-axis at a distance of 20 units on the right hand side of y-axis.
Solution:
We know that the equation of a straight line is parallel and to the right of x-axis at a distance a, then its equation is x = a.
Therefore, the equation of a straight line parallel to y-axis at a distance of 20 units on the right hand side of y-axis is x = 20
● The Straight Line
11 and 12 Grade Math
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