Question

question determine the equation of the circle graphed below. answer attempt 1 out of 2 $(x + 3)^{2}+(y - 1)^{2}=9$ submit answer

Explanation:

Step1: Recall the standard circle equation

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step2: Identify the center from the graph

From the graph, the center of the circle is at \((-3, 1)\) (since it's 3 units left on the x - axis and 1 unit up on the y - axis). So \(h=-3\) and \(k = 1\).

Step3: Determine the radius

Looking at the graph, the radius (distance from center to a point on the circle) is 3 units (since \(r^2=9\), so \(r = 3\)).

Step4: Substitute into the standard equation

Substitute \(h=-3\), \(k = 1\), and \(r = 3\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-3))^2+(y - 1)^2=3^2\), which simplifies to \((x + 3)^2+(y - 1)^2=9\).

Answer:

\((x + 3)^2+(y - 1)^2=9\)