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.

Guest Jul 28, 2020

#1**+1 **

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

Guest Jul 28, 2020