Trying to learn on how to graph a circle.

Question

If possible, can someone explain or teach me how to graph a circle with these given center and radius?

• center A (-2,7) radius;4

• center A (-8,-5) radius;3

• center A (√5, 2√2) radius √10

My teacher in 10th grade didnt taught us how. Thank you.

Answer 1

This is the idea: get a ruler and compass. Draw a coordinate system and with the aid of the ruler mark the location of the center $A$. Now, open the compass along the ruler until it reaches the length of the desired radius$^{1}$, place the pointy end of the compass on top the previously marked center and just draw the circle with the other one.

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$^{1}$ This method with the ruler works out perfectly fine until you find a length that is not a rational number. For that you use Pythagoras' theorem to find the length.

EXAMPLE: Draw a circle of radius $1$ with center $(-1, -\sqrt{2})$

Step 1: Draw a coordinate system

Use the ruler for this one

Step 2: Mark the center of the circle

Here the center requires the length $\sqrt{2}$, remember that $\sqrt{2} = \sqrt{1^2 + 1^2}$, therefore, if we draw a triangle of sides $|\overline{AB}| = 1$ and $|\overline{BC}| = 1$, the hypotenuse will measure $|\overline{AC}| = \sqrt{1^2 + 1^2} = \sqrt{2}$ which is the desired length. So stretch the compass to measure the side $\overline{AC}$ and mark the center of the circle with this number

Step 3: Select the radius and draw the circle

For this last step the radius is just $1$, so we can use the ruler again