To find the equation of xaxis and of a line parallel to xaxis:
Let AB be a straight line parallel to xaxis at a distance b units from it. Then, clearly, all points on the line AB have the same ordinate b. Thus, AB can be considered as the locus of a point at a distance b from xaxis and all points on the line AB satisfy the condition y = b.
Thus, if P(x, y) is any point on AB, then y = b.
Hence, the equation of a straight line parallel to xaxis at a distance b from it is y = b.
The equation of xaxis is y = 0, since, xaxis is a parallel to itself at a distance 0 from it.
Or
Let P (x,y) be any point on the xaxis. Then clearly, for all position of P we shall the same ordinate 0 or, y = 0.
Therefore, the equation of xaxis is y = 0.
If a straight line is parallel and below to xaxis at a distance b, then its equation is y = b.
Solved examples to find the equation of xaxis and equation of a line parallel to xaxis:
1. Find the equation of a straight line parallel to xaxis at a distance of 10 units above the xaxis.
Solution:
We know that the equation of a straight line parallel to xaxis at a distance b from it is y = b.
Therefore, the equation of a straight line parallel to xaxis at a distance 10 units above the xaxis is y = 10.
2. Find the equation of a straight line parallel to xaxis at a distance of 7 units below the xaxis.
Solution:
We know that If a straight line is parallel and below to xaxis at a distance b, then its equation is y = b.
Therefore, the equation of a straight line parallel to xaxis at a distance 7 units below the xaxis is y = 7.
11 and 12 Grade Math
From Equation of a Line Parallel to xaxis to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
