Question

given the equation of the circle below, find the center and radius. ((x + 1)^2 + y^2 = 4) the center is: choose... the radius is: choose... 2 (0, 1) given the follo 16 : sequence: 20, 30, 45, ... what is the co (1, 0) 1.5 what is the val (-1, 0) 159.301

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 \((x + 1)^2 + y^2 = 4\), we can rewrite \((x + 1)^2\) as \((x - (-1))^2\) and \(4\) as \(2^2\). So comparing with the standard form \((x - h)^2 + (y - k)^2 = r^2\), we have \(h = -1\), \(k = 0\), and \(r = 2\). This means the center is \((-1, 0)\) and the radius is \(2\).

Answer:

The center is: \((-1, 0)\)
The radius is: \(2\)