Question

question 4(multiple choice worth 5 points) (07.03 mc) a circular walking path is modeled by ((x + 3)^2 + (y - 4)^2 = 64), where all measurements are in meters. \\(\circ\\) center at \\((-3, 4)\\); \\(r = 8\\) \\(\circ\\) center at \\((-3, 4)\\); \\(r = 64\\) \\(\circ\\) center at \\((3, -4)\\); \\(r = 8\\) \\(\circ\\) center at \\((3, -4)\\); \\(r = 64\\)

Explanation:

Step1: Recall circle equation form

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 \(h\), \(k\), and \(r\)

Given the equation \((x + 3)^2 + (y - 4)^2 = 64\), rewrite \((x + 3)\) as \((x - (-3))\). So, \(h = -3\), \(k = 4\), and \(r^2 = 64\).

Step3: Calculate radius

To find \(r\), take the square root of \(r^2\): \(r = \sqrt{64} = 8\).

Step4: Determine center

The center \((h, k)\) is \((-3, 4)\) since \(h = -3\) and \(k = 4\).

Answer:

A. Center at \((-3, 4)\); \(r = 8\)