Question 1087524
<pre><b>
From the graph below, there are obviously two solutions:

{{{drawing(400,6000/19,-8,11,-4,11,line(-15,-4,15,2), line(0,-17,10,33),
graph(400,6000/19,-8,11,-4,11), circle(-1,4,.1), circle(4,3,.09),
locate(-2.8,4,"(h,k)"), locate(2,4.1,"(4,3)"), circle(4,3,.15),
circle(56/9,23/9,.1),locate(56/9,23/9,"(h,k)"), 
green(line(0,-1,-1,4),line(4,3,56/9,23/9),line(4,3,-1,4)),
circle(56/9,23/9,2.266230895), red(line(4,3,56/9,23/9),line(20/3,1/3,56/9,23/9)),
circle(-1,4,sqrt(26))  )}}}

We set the two green radii, (or the two red radii, equal), and also equate
that to the perpendicular distance from (h,k) to the line 5x - y - 17 = 0

{{{sqrt((h-4)^2+(k-3)^2) = abs(h-5k-5)/sqrt((1)^2+(-5)^2)=abs(5h-k-17)/sqrt((5)^2+(-1)^2)}}}

Set the first two equal, simplify, and square both sides.
Set the second and third equal, simplify, and square both sides.
Solve for one of the letters in one equation.  Substitute it
in the other.

You'll get two solutions for (h,k), and then substitute in one of the
expressions above for the two radii.  Then substitute in the standard 
formula for a circle:

{{{(x-h)^2+(y-k)^2=r^2}}}

to get the two equations.

If you need help solving that, tell me in the thank-you note form 
below and I'll get back to you by email to help you.  No charge ever!

Edwin</pre><b>