The center of a circle and a point on the circle are given. Write the equation of the circle in standard form. center: \( (-5,4) \), point on the circle: \( (-4,4) \) The equation of the circle in standard form is (Type an equation. Simplify your answer.)

To write the equation of a circle in standard form, we use the formula: \[ (x - h)^2 + (y - k)^2 = r^2 \] where \((h, k)\) is the center of the circle and \(r\) is the radius. Given the center of the circle \((-5, 4)\), we have: - \(h = -5\) - \(k = 4\) Next, we need to find the radius \(r\). The radius is the distance from the center of the circle to a point on the circle. The point on the circle is \((-4, 4)\). We can calculate the radius using the distance formula: \[ r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates of the center \((-5, 4)\) and the point on the circle \((-4, 4)\): \[ r = \sqrt{((-4) - (-5))^2 + (4 - 4)^2} \] \[ = \sqrt{(-4 + 5)^2 + (0)^2} \] \[ = \sqrt{(1)^2 + 0} \] \[ = \sqrt{1} = 1 \] Now that we have the radius \(r = 1\), we can substitute \(h\), \(k\), and \(r\) into the standard form equation: \[ (x - (-5))^2 + (y - 4)^2 = 1^2 \] \[ (x + 5)^2 + (y - 4)^2 = 1 \] Thus, the equation of the circle in standard form is: \[ \boxed{(x + 5)^2 + (y - 4)^2 = 1} \]