Question Determine the equation of the circle with center \( (-6,-2) \) containing the point \( (3,-6) \), Answer Attempt 1 out of 4

To find the equation of the circle, we first use the center-radius form of a circle's equation: \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Here, the center is \((-6, -2)\). Next, we find the radius by calculating the distance from the center \((-6, -2)\) to the point \((3, -6)\) using the distance formula: \[r = \sqrt{(3 - (-6))^2 + (-6 - (-2))^2} = \sqrt{(9)^2 + (-4)^2} = \sqrt{81 + 16} = \sqrt{97}.\] Thus, the equation of the circle is: \[(x + 6)^2 + (y + 2)^2 = 97.\] Keep tracking your distance formula skills, as that’s key in geometry! Remember to double-check your calculations! A common mistake is miscalculating either the distance or squaring values incorrectly. It's always best to go step-by-step, reaffirming each part before jumping to the final equation!