Question

what is the diameter of a circle with the equation $(x + 6)^{2}+(y - 4)^{2}=16$?

Explanation:

Step1: Recall the standard form of a circle's 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 radius from the given equation

Given \((x + 6)^2+(y - 4)^2=16\), comparing with the standard form, we have \(r^2 = 16\). So, \(r=\sqrt{16}=4\).

Step3: Calculate the diameter

The diameter \(d\) of a circle is related to the radius \(r\) by the formula \(d = 2r\). Substituting \(r = 4\), we get \(d=2\times4 = 8\).

Answer:

B. 8