Question

write the equation of this circle in standard form.

Explanation:

Step1: Identify center coordinates

The center of the circle is at \((h, k) = (-4, 0)\) (from the graph, the center is on the x - axis at \(x=-4\), \(y = 0\)).

Step2: Determine the radius

The radius \(r\) is the distance from the center \((-4,0)\) to a point on the circle, e.g., \((2,0)\). Using the distance formula \(r=\vert2-(-4)\vert=\vert6\vert = 6\).

Step3: Use the standard circle equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h=-4\), \(k = 0\), and \(r = 6\), we get \((x-(-4))^2+(y - 0)^2=6^2\), which simplifies to \((x + 4)^2+y^2=36\).

Answer:

\((x + 4)^2+y^2=36\)