The choices are missing, but we can solve the problem from the given information
Answer:
The equation which represents the circle is (x - 2)² + (y + 1)² = 16
Step-by-step explanation:
The form of the equation of a circle is (x - h)² + (y - k)² = r², where
- (h , k) are the coordinates of its center
- r is the radius of it
∵ The coordinates of the center of the circle are (2 , -1)
∴ h = 2 and k = -1
The radius of the circle is the segment whose join the center of the circle and any point on the edge of the circle
∵ The circle passes through point (-2 , -1)
∴ The radius of the circle is the distance from the center (2 , -1)
and the point (-2 , -1)
The y-coordinates of the two points are equal that means the radius is a horizontal segment and its length is the difference between their x-coordinates
∵ r = 2 - (-2)
∴ r = 4
Now let us substitute h, k, and r in the form of the equation of the circle
∵ (x - 2)² + (y - -1)² = (4)²
∴ (x - 2)² + (y + 1)² = 16
The equation which represents the circle is (x - 2)² + (y + 1)² = 16
