Question

13 mark for review what is the diameter of the circle in the xy-plane with equation \\((x - 5)^2 + (y - 3)^2 = 16\\)? a 4 b 8 c 16 d 32

Explanation:

Step1: Recall circle equation form

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

Step2: Identify \(r^2\) from given equation

Given \((x - 5)^2 + (y - 3)^2 = 16\), so \(r^2 = 16\).

Step3: Solve for radius \(r\)

Take square root: \(r=\sqrt{16}=4\).

Step4: Calculate diameter

Diameter \(d = 2r\), so \(d = 2\times4 = 8\).

Answer:

B. 8