Question

17.1 equation of a circle
equation. graph the circle.
a. $(x + 3)^2 + (y - 2)^2 = 9$
$(x - h)^2 + (y - k)^2 = r^2$
center: $(-3, 2)$
radius = 3
$r^2 = 9$
$r = 3$
b. $(x + 4)^2 + (y - 8)^2 = 36$
multiple-choice question
lets try letter b.:
what is the center?
(4, -8)
(4, 8)
(-4, -8)
(-4, 8)
rewatch
next question

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: Rewrite given equation

For the equation \((x + 4)^2 + (y - 8)^2 = 36\), rewrite \(x + 4\) as \(x - (-4)\).

Step3: Identify \(h\) and \(k\)

Comparing with \((x - h)^2 + (y - k)^2 = r^2\), we get \(h = -4\) and \(k = 8\). So the center is \((-4, 8)\).

Answer:

D. \((-4, 8)\) (assuming the option with \((-4, 8)\) is labeled D; if the option is labeled as the last one in the list, it's the option with \((-4, 8)\))