The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) .

what is the equation of the circle in standard form?

you don't have to give me the answer, but at least me understand what it is that i need to be looking for in order to solve this problem (step-by-step if it's possible), i'm stuck.

(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

answer: 20

step-by-step explanation:

d

step-by-step explanation: