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1. Identify the center of the circle: The center is given as (-6, -3), so let the center be denoted as (h, k).
2. Determine the radius: The radius (r) is the distance from the center to the given point, which in this case is (-10, 3). We use the distance formula to calculate (r):
[tex]r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]{r = \sqrt{(-10 - (-6))^2 + (3 - (-3))^2} = \sqrt{(-10 + 6)^2 + (3 + 3)^2} = \sqrt{(-4)^2 + (6)^2} = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13}}[/tex]
3. Write the equation of the circle in standard form: The equation of a circle with center (h, k) and radius (r) is given by:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
[tex] \(h = -6\), \(k = -3\), and \: \(r = 2\sqrt{13}\):[/tex]
[tex](x + 6)^2 + (y + 3)^2 = (2\sqrt{13})^2[/tex]
[tex](2\sqrt{13})^2 = 4 \times 13 = 52[/tex]