Question

a circle graphed on a coordinate plane has its center at (2,-4) and a radius of 4 units create an equation of the circle

Answer 1

To create an equation of a circle with center (h, k) and radius r, the general form is:

(x - h)^2 + (y - k)^2 = r^2

Given that the center of the circle is (2, -4) and the radius is 4 units, we can substitute these values into the equation:

(x - 2)^2 + (y - (-4))^2 = 4^2

Simplifying further:

(x - 2)^2 + (y + 4)^2 = 16

So, the equation of the circle is (x - 2)^2 + (y + 4)^2 = 16.