Question

find an equation of the circle having the given graph. express the equation in standard form. the equation of the circle is (type an equation. type your answer in standard form. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Identify center and radius

By observing the graph, assume the center of the circle is \((h,k)\) and radius is \(r\). If the center is at the origin \((0,0)\) (a common - case assumption when no other indication, and if we can count from the grid that the circle is symmetric about the origin) and by counting the grid - squares, the radius \(r = 4\).

Step2: Use standard form of circle equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h = 0\), \(k = 0\), and \(r = 4\) into the equation, we get \((x-0)^2+(y - 0)^2=4^2\).

Answer:

\(x^{2}+y^{2}=16\)