Final answer:
The equation of the circle is x² + (y - 4)² = 36, so the correct option is C.
Step-by-step explanation:
The equation of a circle is a mathematical formula that describes the shape and location of a circle.
The standard equation of a circle is given by: (x - h)^2 + (y - k)^2 = r^2
where:
(h, k) is the center of the circle
r is the radius of the circle
The equation of a circle can also be written in general form as:
x^2 + y^2 + 2gx + 2fy + c = 0
where:
g and f are the coefficients of the x and y terms, respectively
c is the constant term
In this case, the center is 4 units above the origin, which means the center is at (0, 4).
The radius is 6 units, so r = 6. Plugging these values into the equation, we get:
(x - 0)^2 + (y - 4)^2 = 62
Simplifying, we have:
x^2 + (y - 4)2 = 36
Therefore, the equation of the circle is x^2 + (y - 4)^2 = 36, here the correct option will be C.