Answer: (x+1)²+(y-3)²=89
Explanation:
An equation of a circle: (x-a)²+(y-b)=R²
The center of a circle is (-1,3), hence a=-1 b=3
(x-(-1))²+(y-3)=R²
(x+1)²+(y-3)²=R² (1)
Substitute the coordinate (7,-2) belonging to the circle into equation (1):
(7+1)²+(-2-3)²=R²
8²+(-5)²=R²
64+25=R²
89=R²
Thus, R²=89
Hence,
(x+1)²+(y-3)²=89