Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range.
$(x + 1)^{2}+y^{2}=25$
the center is $(-1,0)$.
(type an ordered pair. simplify your answer.)
the radius is $square$.
(type an integer or a simplified fraction.)

Explanation:

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

Given \((x + 1)^{2}+y^{2}=25\), we can rewrite it as \((x-(- 1))^{2}+(y - 0)^{2}=5^{2}\).

Step3: Identify the radius

Comparing with the standard form \((x - h)^{2}+(y - k)^{2}=r^{2}\), we have \(r^{2}=25\). Taking the square root of both sides (since \(r>0\) for a radius), \(r = 5\).

Answer:

The radius is \(5\)