Find an equation of the circle that has center −4, 0 and passes through −2, 3.

The equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Given that the center of the circle is (-4, 0), we can substitute h = -4 and k = 0 into the equation to get (x - (-4))² + (y - 0)² = r², which simplifies to (x + 4)² + y² = r².

We also know that the circle passes through the point (-2, 3). We can substitute x = -2 and y = 3 into the equation to find the radius:

((-2) + 4)² + (3 - 0)² = r² 2² + 3² = r² 4 + 9 = r² r² = 13

Substituting r² = 13 back into the equation of the circle gives us the final equation of the circle:

(x + 4)² + y² = 13.