# Equation of a Line Parallel to y-axis

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