Question

what is the standard form of the equation of the circle to the right? (enter your answer.)

Explanation:

Step1: Identify the center of the circle

Looking at the graph, the center of the circle is at the point \((h, k)\). From the grid, we can see that the center is at \((-2, -3)\) (assuming the x - axis and y - axis grid lines, we count the units from the origin. The x - coordinate of the center is - 2 and the y - coordinate is - 3).

Step2: Determine the radius of the circle

To find the radius, we can count the number of grid units from the center to a point on the circle. Let's take a point on the circle, for example, if we move horizontally from the center \((-2,-3)\) to a point on the circle, we can see that the radius \(r\) is 5 units (by counting the grid squares).

Step3: Use the standard form of the circle's equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius. Substituting \(h=-2\), \(k = - 3\) and \(r = 5\) into the formula, we get \((x-(-2))^2+(y - (-3))^2=5^2\), which simplifies to \((x + 2)^2+(y+3)^2 = 25\).

Answer:

\((x + 2)^2+(y + 3)^2=25\)