Question

question
find the center and radius of the circle represented by the equation below.
$(x + 15)^2 + (y + 5)^2 = 81$
answer attempt 1 out of 2
center: (□,□)
radius: □

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Rewrite the given equation in the standard form

The given equation is \((x + 15)^2 + (y + 5)^2 = 81\). We can rewrite \(x + 15\) as \(x - (-15)\) and \(y + 5\) as \(y - (-5)\). So the equation becomes \((x - (-15))^2 + (y - (-5))^2 = 9^2\) (since \(81 = 9^2\)).

Step3: Identify the center and radius

Comparing with the standard form \((x - h)^2 + (y - k)^2 = r^2\), we have \(h = -15\), \(k = -5\), and \(r = 9\). So the center is \((-15, -5)\) and the radius is \(9\).

Answer:

Center: \((-15, -5)\)
Radius: \(9\)