Question

what is the radius of the circle (x + 4)² + y² = 36? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall the circle equation formula

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: Compare with the given equation

The given equation is \((x + 4)^2 + y^2 = 36\), which can be rewritten as \((x - (-4))^2 + (y - 0)^2 = 6^2\) (since \(36 = 6^2\)). By comparing with the standard form, we can see that \(r^2 = 36\).

Step3: Solve for the radius \(r\)

To find \(r\), we take the square root of both sides of \(r^2 = 36\). So \(r=\sqrt{36}=6\) (we take the positive square root because radius is a non - negative quantity).

Answer:

6