Question

question 8
draw the circle $(x - 1)^2+(y - 3)^2 = 9$.
question help: video

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 circle \((x - 1)^2+(y - 3)^2 = 9\), we have \(h = 1\) and \(k=3\). So the center is \((1,3)\).

Step2: Identify the radius of the circle

Since \(r^2=9\), then \(r=\sqrt{9}=3\).

Step3: Plot the circle

• Plot the center \((1,3)\) on the coordinate plane.
• From the center, move 3 units up (to the point \((1,3 + 3)=(1,6)\)), down (to the point \((1,3-3)=(1,0)\)), left (to the point \((1 - 3,3)=(-2,3)\)) and right (to the point \((1+3,3)=(4,3)\)).
• Sketch the circle passing through these four points.

Answer:

Plot the center at \((1,3)\) and draw a circle with radius \(3\) around it.