Answer:
The answer to your question is (x - 5)² + (y + 5)² = 7
Explanation:
Data
Circle equation (x - 2)² + (y + 4)² = 7
translated (x,y) (x + 3, y - 1)
Process
1.- Find the center of the circle
Remember that the center is represented as (h, k)
From the standard equation
(x - 2)² + (y + 4)² = 7
h = 2
k = -4
Center = (2, -4)
This is the point that is going to change its position
2.- Determine the new coordinates of the center
New center = (2 + 3, -4 - 1)
= (5, -5)
3.- Find the new equation of the circle
(x - 5)² + (y + 5)² = 7