Question

find circle center and radius from equation (conic form)
this is the only question in this section.
question
find the center and radius of the circle represented by the equation below.
$(x - 10)^2 + (y - 5)^2 = 144$
answer attempt 1 out of 2
center: (□,□)
radius: □

Explanation:

Step1: Recall the standard circle 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: Identify \(h\), \(k\), and \(r\) from the given equation

Given the equation \((x - 10)^2 + (y - 5)^2 = 144\), we can compare it to the standard form. Here, \(h = 10\), \(k = 5\), and \(r^2 = 144\).

Step3: Calculate the radius

To find \(r\), we take the square root of \(r^2\). So, \(r=\sqrt{144}=12\).

Answer:

Center: \((10, 5)\)
Radius: \(12\)