Question

write the equation of this circle in standard form.

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 of the circle

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

Step3: Determine the radius of the circle

Looking at the graph, the circle extends from \(x = -1\) to \(x = 1\) (or \(y = -1\) to \(y = 1\)), so the radius \(r = 1\).

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

Substituting \(h = 0\), \(k = 0\), 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:

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