Question

what is the diameter of this circle?

Explanation:

Step1: Identify the radius

The center of the circle is at \((-4, 0)\). One point on the circle is at \((0, 0)\) (where the circle intersects the y - axis) or at \((-8, 0)\) (where the circle intersects the x - axis). Let's use the points \((-4, 0)\) (center) and \((0, 0)\) (point on the circle). The distance between these two points is the radius \(r\). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \((x_1,y_1)=(-4,0)\) and \((x_2,y_2)=(0,0)\), we have \(r=\sqrt{(0 - (-4))^2+(0 - 0)^2}=\sqrt{4^2}=4\). Alternatively, we can see from the x - axis: the center is at \(x=-4\) and the leftmost point is at \(x = - 8\), so the radius is \(\vert-4-(-8)\vert=4\).

Step2: Calculate the diameter

The formula for the diameter \(d\) of a circle is \(d = 2r\). Since \(r = 4\), then \(d=2\times4 = 8\).

Answer:

8