Question

question determine the equation of the circle graphed below.
answer attempt 1 out of 2
$(x + 3)^{2}+(y - 1)^{2}=$ 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, we can see that the radius (distance from center to a point on the circle) is 4 units (by counting the grid squares or using distance formula, but visually it's clear). So \(r = 4\), and \(r^2=16\).

Step4: Substitute into the standard equation

Substitute \(h=-3\), \(k = 1\) and \(r^2 = 16\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-3))^2+(y - 1)^2=16\), which simplifies to \((x + 3)^2+(y - 1)^2=16\).

Answer:

\((x + 3)^2+(y - 1)^2 = 16\)