12.3 Homework: circles

Write down the equation for a circle (*aka “All the Points Equidistant from a Given Point”) with center (–3,–6) and radius 9. (Although the wording is different, this is exactly like the problems you did on the in-class assignment.)

Now, let’s take it the other way. ${(x–4)}^2+{(y+8)}^2=49$ is the equation for a circle.

• A

  What is the center of the circle?

• B

  What is the radius?

• C

  Draw the circle.

• D

  Find two points on the circle (by looking at your drawing) and plug them into the equation to make sure they work. (Show your work!)

$3x^2+3y^2+18x+30y–6=0$

• A

  Complete the square—as I did above—to put this into the form: ${(x–h)}^2+{(y–k)}^2=r^2$ .

• B

  What are the center and radius of the circle?

• C

  Draw the circle.

• D

  Find two points on the circle (by looking at your drawing) and plug them into original equation to make sure they work. (Show your work!)