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: Determine the center of the circle

The center of the circle \((h,k)\) is at \((-2,-5)\) as observed from the graph.

Step2: Determine the radius of the circle

Count the units from the center \((-2,-5)\) to a point on the circle. For example, from \((-2,-5)\) to \((-1,-1)\) (or other points on the circle), the radius \(r = 5\) (using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), but by counting grid - units it's straightforward here).

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 \(h=-2\), \(k = - 5\), and \(r = 5\) into the formula:

$$
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$$

Answer:

\((x + 2)^2+(y + 5)^2=25\)