Find an equation of the circle that has center −6, 5 and passes through −2, 1.

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

Step 1: Identify the center of the circle The center of the circle is given as (-6, 5). So, h = -6 and k = 5.

Step 2: Find the radius of the circle The circle passes through the point (-2, 1). The radius of the circle is the distance between the center of the circle and any point on the circle. We can use the distance formula to find the radius: r = sqrt[(x2 - x1)² + (y2 - y1)²]

Substituting the given points into the distance formula gives: r = sqrt[(-2 - (-6))² + (1 - 5)²] = sqrt[(4)² + (-4)²] = sqrt[16 + 16] = sqrt[32] = 4sqrt(2)

Step 3: Substitute h, k, and r into the equation of the circle Substituting h = -6, k = 5, and r = 4sqrt(2) into the equation of the circle gives: (x - (-6))² + (y - 5)² = (4sqrt(2))²

Simplifying this gives the equation of the circle as: (x + 6)² + (y - 5)² = 32.