Question

draw the circle $(x - 3)^{2}+(y - 1)^{2}=1$.

Explanation:

Step1: Identify the center of the circle

The standard form of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center. For the equation \((x - 3)^2+(y - 1)^2 = 1\), \(h = 3\) and \(k=1\). So the center is \((3,1)\).

Step2: Identify the radius of the circle

From the standard form \((x - h)^2+(y - k)^2=r^2\), comparing with \((x - 3)^2+(y - 1)^2 = 1\), we have \(r^2=1\), so \(r = 1\).

Step3: Plot the circle

• Plot the center \((3,1)\) on the coordinate plane.
• From the center, move 1 unit up, down, left, and right (since the radius \(r = 1\)). The points will be \((3,2)\), \((3,0)\), \((2,1)\), and \((4,1)\).
• Sketch the circle passing through these four points.

Answer:

Plot a circle with center \((3,1)\) and radius \(1\) on the given coordinate - plane.