Question

what is the equation of the circle? enter an answer in each box to complete the equation. be sure to include a plus or minus symbol where needed. (x (square))²+(y (square))²=(square)

Explanation:

Step1: Recall the standard - form of a circle equation

The standard - form of the equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\).

Step2: Identify the center and radius from the graph

If the center of the circle is at the origin \((0,0)\) (assuming no other information about the center is given from the graph and it appears to be centered at the origin) and the radius \(r\) is measured from the center to a point on the circle. Let's assume the radius \(r = 2\) (by counting the grid - units).

Step3: Substitute values into the equation

Substituting \(h = 0\), \(k = 0\), and \(r = 2\) into the standard - form equation \((x - h)^2+(y - k)^2=r^2\), we get \((x-0)^2+(y - 0)^2=2^2\), which simplifies to \(x^{2}+y^{2}=4\).

Answer:

\((x - 0)^2+(y - 0)^2=4\)