Question

a) find the center - radius form of the equation of the circle with center (-1,1) and radius 4.
b) graph the circle.
a) the center - radius form of the equation of the circle is □.
(type an equation.)

Explanation:

Step1: Recall the center - radius form of a circle's equation

The center - radius 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: Substitute the given values into the formula

Given \(h=-1\), \(k = 1\), and \(r = 4\). Substitute these into \((x - h)^2+(y - k)^2=r^2\).
We get \((x-(-1))^2+(y - 1)^2=4^2\).
Simplify \((x + 1)^2+(y - 1)^2=16\).

Answer:

\((x + 1)^2+(y - 1)^2=16\)