Answer:

The equation of a circle passing through the coordinates of the end points of diameters is (x – x₁) (x – x₂) + (y – y₁)(y – y₂) = 0

Substituting the values:(x₁, y₁) = (5, – 3) & (x₂, y₂) = (2, – 4)

(x – 5)(x – 2) + (y + 3)(y + 4) = 0

x² – 2x – 5x + 10 + y² + 3y + 4y + 12 = 0

x² + y² – 7x + 7y + 22 = 0