Find the equation for the circle with center (-2, -5) and padding through (5, -4)

1. Identify the center of the circle \((h, k)\):
h = -2
k = -5

2. Use the distance formula to find the radius \( r \):
The point on the circle is \( (x_1, y_1) = (5, -4) \).

r = \sqrt{(x_1 - h)^2 + (y_1 - k)^2}

Substitute the values:
r = \sqrt{(5 - (-2))^2 + (-4 - (-5))^2}
r = \sqrt{(5 + 2)^2 + (-4 + 5)^2}
r = \sqrt{7^2 + 1^2}
r = \sqrt{49 + 1}
r = \sqrt{50}
r = \sqrt{50}

3. Substitute \( h \), \( k \), and \( r^2 \) into the equation of a circle \((x - h)^2 + (y - k)^2 = r^2\):
(x + 2)^2 + (y + 5)^2 = 50

The equation of the circle is:
(x + 2)^2 + (y + 5)^2 = 50