Question

the equation of a circle is given.
$(x - 2)^2 + (y - 1)^2 = 9$
complete the sentence to describe the circle.
the circle has a center at (3, 2) and a radius of 5 units.

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 \((x - 2)^2 + (y - 1)^2 = 9\), we can compare it to the standard form. Here, \(h = 2\), \(k = 1\), and \(r^2 = 9\), so \(r=\sqrt{9}=3\).

Answer:

The circle has a center at \((2, 1)\) and a radius of \(3\) units.