Answer:
(x + 2)² + (y + 5)² = 25
Step-by-step explanation:
The circle is tangent to the x-axis at (-2, 0). This means the center of the circle must be directly above or below this point. So the x-coordinate of the center is -2.
Since the center of the circle is on the line y = 3x + 1, we can find the y-coordinate:
y = 3(-2) + 1
y = -5
The center of the circle is (-2, -5). The distance between the center and the point (-2, 0) is 5 units. This is the radius of the circle.
We can now write the equation of the circle:
(x − h)² + (y − k)² = r²
(x + 2)² + (y + 5)² = 25
Graph:
desmos.com/calculator/wzionolfli
