Question

practice
graph a circle that has its center at (0,0) and passes through (2,2). you can practice moving one of the points and then move it back. when the drawing looks correct, click submit.
clear all draw:
question help: video 1 video 2
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Explanation:

Step1: Calculate circle radius

Use distance formula for $(0,0)$ and $(2,2)$:
$$r = \sqrt{(2-0)^2 + (2-0)^2} = \sqrt{4+4} = \sqrt{8} = 2\sqrt{2}$$

Step2: Write circle equation

Standard form for center $(h,k)$:
$$(x-h)^2 + (y-k)^2 = r^2$$
Substitute $(h,k)=(0,0), r^2=8$:
$$x^2 + y^2 = 8$$

Step3: Identify key plot points

Points on the circle include:
$(2\sqrt{2},0) \approx (2.83,0)$, $(0,2\sqrt{2}) \approx (0,2.83)$, $(-2\sqrt{2},0) \approx (-2.83,0)$, $(0,-2\sqrt{2}) \approx (0,-2.83)$, and the given $(2,2)$.

Step4: Plot and draw the circle

Mark the center $(0,0)$, plot the key points, then use the circle drawing tool to connect them smoothly.

Answer:

The circle has the equation $x^2 + y^2 = 8$, centered at $(0,0)$ with radius $2\sqrt{2} \approx 2.83$. To draw it:

1. Mark the center at the origin $(0,0)$.
2. Plot the point $(2,2)$ and additional points like $(2.83, 0)$, $(0, 2.83)$, $(-2.83, 0)$, $(0, -2.83)$.
3. Use the circle drawing tool to create a smooth circle passing through all these points with the center at $(0,0)$.