Question 968855
Each point on the edge of a circle is equidistant from the center of the circle.
The center of a circle is located at (6, 3). Which point on the y-axis could be
on the edge of the circle if the distance from the center of the circle to the
edge is 10 units?
<pre>
This describes a circle with center (h,k) = (6,3) and radius r = 10

That circle has the equation  

(x-h)²+(y-k)² = r²

(x-6)²+(y-3)² = 10²

(x-6)²+(y-3)² = 100

Every point on the y-axis has 0 as its x-coordinate, so we
substitute x=0 in

(x-6)²+(y-3)² = 100

(0-6)²+(y-3)² = 100
 
 (-6)²+(y-3)² = 100

    36+(y-3)² = 100

       (y-3)² = 64

          y-3 = ±8

            y = 3±8

      y=3+8,  y=3-8
      y=11,   y=-5

Two solutions: (0,11) and (0,-5)

{{{drawing(400,400,-5,17,-8,14, graph(400,400,-5,17,-8,14),

circle(6,3,10.1),

circle(6,3,0.15),circle(6,3,0.13),circle(6,3,0.11),circle(6,3,0.09),circle(6,3,0.07),circle(6,3,0.05),circle(6,3,0.03),circle(6,3,0.01),
locate(6,3,"(6,3)"),
green(line(6,3,0,11),line(6,3,0,-5)),
locate(0.2,-4.5,"(0,-5)"),locate(0.2,11.3,"(0,11)"),
green(locate(3.1,7.5,10),locate(3,-1,10)),
circle(0,11,0.15),circle(0,11,0.13),circle(0,11,0.11),circle(0,11,0.09),circle(0,11,0.07),circle(0,11,0.05),circle(0,11,0.03),circle(0,11,0.01),
circle(0,-5,0.15),circle(0,-5,0.13),circle(0,-5,0.11),circle(0,-5,0.09),circle(0,-5,0.07),circle(0,-5,0.05),circle(0,-5,0.03),circle(0,-5,0.01) )}}}

Edwin</pre>