Question 1043671
<pre><b>
All points on the x-axis have their y-coordinates equal to 0.
So let the point (a,0) be a point on the x-axis such that the
distance from (12,5) to (a,0) is 13 units:

Use the distance formula:

{{{d=sqrt((x[2]-x[1])^2+(y[2]-y[1])^2)}}}

{{{(12-a)^2+(5-0)^2=13}}}

Square both sides:

{{{(12-a)^2+5^2=13^2}}}

{{{(12-a)^2+25=169}}}

(((12-a)^2=144}}}

Take square roots of both sides

{{{12-a="" +- 12}}}

Using the +

{{{12-a=12}}}

{{{-a=0}}}

{{{a=0}}}

Using the -

{{{12-a=-12}}}

{{{-a=-24}}}

{{{a=24}}}

There are exactly two points, substituting in (a,0),

they are (0,0), and (24,0)

{{{drawing(400,10800/29,-2,27,-9,18,locate(16.5,4,13), locate(6,4,13),
locate(12,6,"(12,5)"),graph(400,10800/29,-2,27,-9,18),arc(12,5,26,-26,195,208),circle(12,5,.2),  locate(24,1,"(24,0)"),circle(0,0,.2), circle(24,0,.2),
line(0,0,12,5),line(24,0,12,5),arc(12,5,26,-26,330,345),green(circle(12,5,13))

  )}}}


Edwin</pre>