Find all the points that are on the x-axis that are a distance of 13 units from the point (12,-5).

Let point A(x,y) be the point on the x-axis. All points that lie on the x-axis have y-coordinate equal to 0, then A(x,y).

Find the distance from point A to point (12,-5):

This distance is equal to 13, then

You get two ponts (0,0) and (24,0).

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c