Write an equation in standard form of a circle with the given center and radius. center (0,0); radius 4

The equation in standard form of a circle with center (0,0) and radius 4 is:

x^2 + y^2 = 16

show your work please!

Sure, here's how to arrive at the equation:

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.

The equation of a circle in standard form is:

(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.

To write an equation of a circle in standard form, we can use the formula:

(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.