Question

write an equation that represents the graph of the circle in standard form.
the equation of the circle in standard form is

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Identify the center \((h,k)\)

From the graph, the center of the circle is \((0,0)\), so \(h = 0\) and \(k = 0\).

Step3: Determine the radius \(r\)

The radius \(r\) is the distance from the center to a point on the circle. Observing the graph, \(r = 1\).

Step4: Substitute \(h\), \(k\), and \(r\) into the standard form

Substitute \(h = 0\), \(k = 0\), and \(r = 1\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 0)^2+(y - 0)^2=1^2\), which simplifies to \(x^{2}+y^{2}=1\).

Answer:

\(x^{2}+y^{2}=1\)