Question

which equation describes a circle with a radius of 4 and a center located at $(-5, 2)$?

• $(x + 5)^2 + (y - 2)^2 = 4$
• $(x - 5)^2 + (y + 2)^2 = 16$
• $(x + 5)^2 + (y - 2)^2 = 16$
• $(x - 5)^2 + (y + 2)^2 = 4$

Explanation:

Step1: Recall the circle equation formula

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

Step2: Identify the center and radius values

Given the center is \((-5, 2)\), so \(h = -5\) and \(k = 2\). The radius \(r = 4\), so \(r^2 = 4^2 = 16\).

Step3: Substitute \(h\), \(k\), and \(r^2\) into the formula

Substitute \(h = -5\), \(k = 2\), and \(r^2 = 16\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - (-5))^2 + (y - 2)^2 = 16\), which simplifies to \((x + 5)^2 + (y - 2)^2 = 16\).

Answer:

\(\boldsymbol{(x + 5)^2 + (y - 2)^2 = 16}\) (corresponding to the third option)