A circle passes through the point (12,0), and is tangent to the y-axis at the point (0,3), as shown. Find the radius of the circle.
he circle is tangent to the y-axis at (0, 2) , so the y-coordinate of the center must be 2 .
We know..
(x - h)2 + (y - 2)2 = r2 , where h is the x-coordinate of the vertex and r is the radius.
(0 - h)2 + (2 - 2)2 = r2 → h2 = r2 → h = ± r
(8 - h)2 + (0 - 2)2 = r2 → (8 - h)2 + 4 = r2
In the last equation, substitute ± r in for h .
(8 - ± r)2 + 4 = r2
(8 + r)2 + 4 = r2 or (8 - r)2 + 4 = r2
64 + 16r + r2 + 4 = r2 64 - 16r + r2 + 4 = r2
68 + 16r = 0 68 - 16r = 0
r = -68/16 r = 68/16
r = -4.25 r = 4.25
Since r is a distance, r = 4.25
It's not possible!!!! The diameter is over 12 units.
