Equation of a Circle

Using the following equations, find the center and radius of the circle:

  1. $(x-5)^2+(y-9)^2=81$: center: (5, 9), radius: 9
  2. $(x-2)^2+(y-4)^2=25$ center: (2, 4), radius: 5
  3. $(x+4)^2+(y-7)^2=49$ center: (-4, 7), radius: 7
  4. $(x+6)^2+(y+1)^2=16$ center: (-6, -1), radius: 4

Graph the following circles: 

  1. $(x+3)^2+(y+2)^2=4$ 

    Graphed circle #5

  2. $(x-1)^2+(y-1)^2=9$ 

    Graphed circle #6

  3. $(x+2)^2+(y+1)^2=16$ 

    Graphed circle #7

Test to see if the following points are on the circle with equation $(x-4)^2+(y-5)^2=81$:

  1. $(13,14)$ No  $\eqalign{(13-4)^2+(14-5)^2=81\\9^2+9^2=81\\81+81=81\\162 \neq 81}$


     
  2. $(4,-4)$ Yes $\eqalign{(4-4)^2+(-4-5)^2=81\\0^2+(-9)^2=81\\0+81=81\\81=81 81}$ 


     
  3. $(2,2)$ No $\eqalign{(2-4)^2+(2-5)^2=81\\(-2)^2+(-3)^2=81\\4+9=81\\13 \neq 81}$


     
  4. $(0,5)$ No $\eqalign{(0-4)^2+(5-5)^2=81\\(-4)^2+0^2=81\\16+0=81\\16 \neq 81}$


     

Write the equations for the following circles:

  1. Graphed circle #1


    $h=-2, k=3, r=2 \rightarrow (x+2)^2+(y-3)^2=4$

     

  2. Graphed circle #2
    $h=0, k=-3, r=4 \rightarrow (x-0)^2+(y+3)^2=4$

     
  3. Graphed circle #3
    $h=4, k=-2, r=1 \rightarrow (x-4)^2+(y+2)^2=1$

     

  4. Graphed circle #4
    $h=0, k=1, r=5 \rightarrow (x-0)^2+(y-1)^2=25$


    Graphed circle #5

    $h=-4, k=-4, r=2 \rightarrow (x+4)^2+(y+4)^2=4$