Questions: Use the graph to find the standard equation of the circle. Write the equation of the circle in standard form (x-2)^2 + (y+1)^2 = 9

Solution Steps

From the graph, identify the center \((h, k)\) and the radius \(r\) of the circle. The center appears to be at \((2, -3)\) and the radius is 4 units.

The standard form of the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\). Substitute \(h = 2\), \(k = -3\), and \(r = 4\) into the equation.

Substitute the values into the standard form equation: \[ (x - 2)^2 + (y + 3)^2 = 4^2 \] Simplify \(4^2\) to get 16: \[ (x - 2)^2 + (y + 3)^2 = 16 \]

Final Answer