To find the equation of the circle, we start by identifying two key elements based on the information given: the center of the circle and the radius.
The center of the circle is given as (3, 8). The radius can be determined because the circle is tangent to the x-axis. The distance from the center of the circle to the x-axis is equal to the y-coordinate of the center, which is 8. Therefore, the radius of the circle is 8.
Having the center and radius, we can use the standard form of the equation of a circle, which is:
(x – h)² + (y – k)² = r²
Here, (h, k) represents the center of the circle, and r represents the radius. Substituting the values we have:
– h = 3
– k = 8
– r = 8
Plugging these into the equation gives:
(x – 3)² + (y – 8)² = 8²
Therefore, we simplify this to:
(x – 3)² + (y – 8)² = 64
This is the standard form of the equation of the circle centered at (3, 8) and tangent to the x-axis.