Questions: Graph the circle given below by moving the key points: (x-4)^2+(y+3)^2=4 To graph the circle, drag the center point to the desired location, and then drag the radius point until the radius is the desired number of units.

Solution Steps

The given equation of the circle is \((x - 4)^2 + (y + 3)^2 = 4\). This is in the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. From the equation, we can identify:

• \(h = 4\)
• \(k = -3\)

So, the center of the circle is \((4, -3)\).

The right side of the equation is \(4\), which represents \(r^2\). To find the radius \(r\), we take the square root of \(4\): \[ r = \sqrt{4} = 2 \]

To graph the circle:

1. Place the center of the circle at \((4, -3)\) on the coordinate plane.
2. From the center, measure a distance of 2 units in all directions to draw the circle.

Final Answer