Answer:
The equation of the circle is;
(x - 2)² + (y - 4)² = 5²
Step-by-step explanation:
We note that the general equation of a circle is given as follows;
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The radius of the circle
The given parameters are;
The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool
The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation
Taking the center of the pool as the origin of the coordinate plane system, we have;
The coordinate of the center of the circle = The coordinate of their motion from the center of the circle
∴ The coordinate of the center of the circle = (2, 4)
∴ (h, k) = (2, 4)
h = 2, k = 4
The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)
∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5
r = 5
The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;
(x - 2)² + (y - 4)² = 5².
has a unique root, 
, for any 
is a polynomial with roots 
and 
