To write the equation of a circle, we use the standard form of the equation:
(x – h)² + (y – k)² = r²
Where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is given as (3, 8), so h = 3 and k = 8.
Next, we need to determine the radius (r). A circle that is tangent to the x-axis means that the distance from the center of the circle to the x-axis is equal to the radius. Since the center is located at (3, 8), the distance from the center to the x-axis (y = 0) is simply the y-coordinate of the center, which is 8.
Therefore, the radius of our circle is:
r = 8
Now we can substitute the center and the radius into the standard form of the equation:
(x – 3)² + (y – 8)² = 8²
This simplifies to:
(x – 3)² + (y – 8)² = 64
So, the equation of the circle centered at (3, 8) and tangent to the x-axis in standard form is:
(x – 3)² + (y – 8)² = 64