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A circle passes through the point (12,0), and is tangent to the y-axis at the point (0,8). Find the radius of the circle.

 Jul 10, 2021
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The center is (a, 8) since it is tangent to the y-axis at the point (0,8). 

Since (12, 0) and (0, 8) both touch it, the center is the same distance from them. 

sqrt((12-a)^2 + (8-0)^2) = sqrt((a-0)^2 + (8-8)^2)

144 - 24a + a^2 + 64 = a^2 + 0

a = 26/3

(26/3, 8) is the center of the circle. 

The radius is the distance from the center to one of the points, (26/3, 8) to (0, 8) has a distance of 26/3.

 

 

=^._.^=

 Jul 10, 2021

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