The equation in standard form of a circle with center (0,0) and radius 4 is:
x^2 + y^2 = 16
x^2 + y^2 = 16
The standard form of a circle equation is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is its radius.
In this case, we have:
center = (0,0)
radius = 4
So we can plug these values into the standard form equation and get:
(x - 0)^2 + (y - 0)^2 = 4^2
Simplifying, we get:
x^2 + y^2 = 16
This is the equation in standard form for a circle with center (0,0) and radius 4.
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the coordinates of the center of the circle, and r is the radius.
Using the given information, the equation of the circle with center (0,0) and radius 4 can be written as:
(x - 0)^2 + (y - 0)^2 = 4^2
Simplifying the equation gives:
x^2 + y^2 = 16
Thus, the equation in standard form of the circle with center (0,0) and radius 4 is x^2 + y^2 = 16.
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the center of the circle, and r represents the radius.
Given that the center is (0,0) and the radius is 4, we can substitute these values into the formula:
(x - 0)^2 + (y - 0)^2 = 4^2
Simplifying this equation gives us:
x^2 + y^2 = 16
Therefore, the equation in standard form of a circle with center (0,0) and radius 4 is x^2 + y^2 = 16.