Final answer:
The equation of the circle with center on y=4 and tangent to the x-axis at (-2,0) is (x+2)² + (y-4)² = 16. The center of the circle is (-2, 4), and the radius is 4 units.
Step-by-step explanation:
To find an equation of the circle with its center on y=4 and tangent to the x-axis at (-2, 0), we first determine the radius of the circle. Since it is tangent at the point (-2, 0), the radius is the vertical distance from the center of the circle to the point of tangency, which is 4 units because the center lies on the line y = 4. Thus, the center of the circle is at (-2, 4).
The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Plugging in the values we have, the equation of the circle is (x + 2)² + (y - 4)² = 4².
When you sketch this circle, it will appear above the x-axis, just touching it at the point (-2, 0).