Answer
Option A is correct.
The equation of the circle shown in general form is
x² + y² + 4x - 2y - 4 = 0
Step-by-step explanation
The equation of a circle with center (h, k) and radius r is given as
(x - h)² + (y - k)² = r²
For this question,
Center = (h, k) = (-2, 1)
h = -2, k = 1
Radius = 3 units (Distance from the center of the circle to any point on the circumference of the circle)
(x - h)² + (y - k)² = r²
(x - (-2))² + (y - 1)² = 3²
(x + 2)² + (y - 1)² = 9
x² + 4x + 4 + y² - 2y + 1 = 9
x² + y² + 4x - 2y + 4 + 1 - 9 = 0
x² + y² + 4x - 2y - 4 = 0
Hope this Helps!!!