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: Find the center of the circle

The center of the circle \((h,k)\) is \((-2,-3)\) (from the graph).

Step2: Find the radius of the circle

The radius \(r\) is \(3\) (distance from center to a point on the circle, for example, from \((-2,-3)\) to \((1,-3)\) is \(3\) units).

Step3: Use the standard form of the circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\). Substitute \(h=-2\), \(k = - 3\), and \(r = 3\) into the equation:

$$
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Answer:

\((x + 2)^2+(y + 3)^2=9\)