Question

center-radius form: $(x - h)^2+(y - k)^2=r^2$
use the graph of a circle to list the center, radius, and equation in center - radius form.
1.

center:
radius:
equation:

2.

center:
radius:
equation:

write equation in center - radius form and graph given center and radius.

1. given: center: $(0,3)$ radius: $r = 3$

equation:

1. given: center: $(-2,-3)$ radius: $r = 4$

equation:

Explanation:

1.

Step1: Find the center

The center of a circle is the point \((h,k)\). From the graph, the center is \((1, - 1)\).

Step2: Find the radius

Count the distance from the center to a point on the circle. The radius \(r = 3\).

Step3: Write the equation

Using the center - radius form \((x - h)^{2}+(y - k)^{2}=r^{2}\), substitute \(h = 1\), \(k=-1\) and \(r = 3\).
\((x - 1)^{2}+(y + 1)^{2}=9\)

2.

Step1: Find the center

From the graph, the center is \((0,0)\).

Step2: Find the radius

Count the distance from the center to a point on the circle. The radius \(r = 2\).

Step3: Write the equation

Using the center - radius form \((x - h)^{2}+(y - k)^{2}=r^{2}\), substitute \(h = 0\), \(k = 0\) and \(r = 2\).
\(x^{2}+y^{2}=4\)

3.

Step1: Write the equation

Given center \((h,k)=(0,3)\) and radius \(r = 3\). Using the center - radius form \((x - h)^{2}+(y - k)^{2}=r^{2}\), substitute \(h = 0\), \(k = 3\) and \(r = 3\).
\((x-0)^{2}+(y - 3)^{2}=9\) or \(x^{2}+(y - 3)^{2}=9\)

4.

Step1: Write the equation

Given center \((h,k)=(-2,-3)\) and radius \(r = 4\). Using the center - radius form \((x - h)^{2}+(y - k)^{2}=r^{2}\), substitute \(h=-2\), \(k =-3\) and \(r = 4\).
\((x + 2)^{2}+(y + 3)^{2}=16\)

Answer:

1.

• Center: \((1,-1)\)
• Radius: \(3\)
• Equation: \((x - 1)^{2}+(y + 1)^{2}=9\)

2.

• Center: \((0,0)\)
• Radius: \(2\)
• Equation: \(x^{2}+y^{2}=4\)

1. Equation: \(x^{2}+(y - 3)^{2}=9\)
2. Equation: \((x + 2)^{2}+(y + 3)^{2}=16\)