A circle centered at point o (2; -4) intersects the ordinate at point a (0; 5) write the equation of the circle.

Find the square of the radius of the circle if the coordinates of its center O and point A lying on it are known:
O (2; -4);
A (0; 5);
R ^ 2 = (x (A) – x (O)) ^ 2 + (y (A) – y (O)) ^ 2;
R ^ 2 = (0 – 2) ^ 2 + (5 + 4) ^ 2 = 2 ^ 2 + 9 ^ 2 = 4 + 81 = 85.
Let’s compose the equation of the circle using the formula:
(x – x (O)) ^ 2 + (y – y (O)) ^ 2 = R ^ 2;
(x – 2) ^ 2 + (y + 4) ^ 2 = 85.
Answer: (x – 2) ^ 2 + (y + 4) ^ 2 = 85.