A circle in the -plane has its center at and radius . What is an equation of the circle?

Identify center and radius: Identify the center and radius of the circle. The center is at (0,0) and the radius is 2. Use standard form equation: Use the standard form equation for a circle, (x - h)^2 + (y - k)^2 = r^2, where h and k are the coordinates of the center and r is the radius. Substitute values into equation: Substitute the values into the equation: h = 0, k = 0, r = 2. So, (x - 0)^2 + (y - 0)^2 = 2^2. Simplify the equation: Simplify the equation: x^2 + y^2 = 4.

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A circle in the $xy$ -plane has its center at $(h, k)$ and radius $r$ . What is an equation of the circle?

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Algebra 2

Write equations of circles in standard form using properties

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Q. A circle in the

xy

-plane has its center at

(h, k)

and radius

r

. What is an equation of the circle?

Identify center and radius: Identify the center and radius of the circle. The center is at $(0,0)$ and the radius is $2$ .
Use standard form equation: Use the standard form equation for a circle, $(x - h)^2 + (y - k)^2 = r^2$ , where $h$ and $k$ are the coordinates of the center and $r$ is the radius.
Substitute values into equation: Substitute the values into the equation: $h = 0$ , $k = 0$ , $r = 2$ . So, $(x - 0)^2 + (y - 0)^2 = 2^2$ .
Simplify the equation: Simplify the equation: $x^2 + y^2 = 4$ .