Question

question 1 2 pts identify the center and radius of the circle $(x + 4)^{2}+(y - 2)^{2}=16$ a. center: $(-4,2),r = 4$ b. center: $(4,2),r = 4$ c. center: $(4,-2),r = 16$ d. center: $(4,-2),r = 4$

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: Rewrite the given equation in the standard form

Given \((x + 4)^2+(y - 2)^2=16\), we can rewrite \((x + 4)\) as \((x-(-4))\) and \(16\) as \(4^2\). So the equation becomes \((x-(-4))^2+(y - 2)^2=4^2\).

Step3: Identify the center and radius

Comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h=-4\), \(k = 2\), and \(r = 4\).

Answer:

A. Center: \((-4,2)\), \(r = 4\)