Thread: Locus question #1

My question is:

Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please

Originally Posted by moeyfrompunchy

My question is:

Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please

In order for point P to be equidistant from the x and y-axis, it has to move along the line y=x.

Hello, moeyfrompunchy!

Did you even bother to make a sketch?

Find the equation of the locus of a point
that moves so that it is equidistant from the -axis and the -axis.

Code:

      |         P
    B + - - - - *(x,y)
      |    x    :
      |         :
      |         : y
      |         :
      |         :
  ----+---------+----
      |         A
      |

The point is

Its distance from the -axis is: .

Its distance from the -axis is: .

We want these distances to be equal: .


How hard was that?

Originally Posted by moeyfrompunchy

My question is:

Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please

1. If the point P has equal distances from the axes then you have:



2. If you write this equation without the absolute values you'll get as the locus l: