Question

Line l is parallel to y-axis and at a distance of 2 units to the left. Write its equation. Plz...

Answer 1

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.

Equation of a Line Parallel to y-axis
Equation of a Line Parallel to y-axis
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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.