About Graphing Circles:

In some cases, we will need to find the equation of a circle in center-radius form, otherwise known as standard form. Additionally, we may need to use the equation of a circle in center-radius form to graph circles on the coordinate plane.


Test Objectives
  • Demonstrate the ability to write the equation of a circle in standard form
  • Demonstrate the ability to write the equation of a circle in general form
  • Demonstrate the ability to graph a circle
Graphing Circles Practice Test:

#1:

Instructions: find the center-radius form.

$$a)\hspace{.2em}x^2 + y^2 + 12x - 2y + 12=0$$

$$b)\hspace{.2em}x^2 + y^2 - 28x - 14y + 236=0$$

$$c)\hspace{.2em}x^2 + y^2 - 4x - 14y + 4=0$$


#2:

Instructions: write each equation in general form.

$$a)\hspace{.2em}(x - 16)^2 + (y - 11)^2=9$$

$$b)\hspace{.2em}(x + 8)^2 + (y - 3)^2=44$$

$$c)\hspace{.2em}(x + 10)^2 + (y - 9)^2=49$$


#3:

Instructions: find the x and y intercepts.

$$a)\hspace{.2em}x^2 + y^2=49$$

$$b)\hspace{.2em}x^2 + y^2 + 30x + 22y + 342=0$$


#4:

Instructions: graph each circle.

$$a)\hspace{.2em}x^2 + y^2 + 6x + 8y + 21=0$$


#5:

Instructions: graph each circle.

$$a)\hspace{.2em}x^2 + y^2 - 2x + 6y + 1=0$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}(x + 6)^2 + (y - 1)^2=25$$

$$b)\hspace{.2em}(x - 14)^2 + (y - 7)^2=9$$

$$c)\hspace{.2em}(x - 2)^2 + (y - 7)^2=49$$


#2:

Solutions:

$$a)\hspace{.2em}x^2 + y^2 -32x - 22y + 368=0$$

$$b)\hspace{.2em}x^2 + y^2 + 16x - 6y + 29=0$$

$$c)\hspace{.2em}x^2 + y^2 + 20x - 18y + 132=0$$


#3:

Solutions:

$$a)\hspace{.2em}$$ $$x-intercepts: (7,0), (-7,0) $$ $$ y-intercepts: (0,7), (0,-7)$$

$$b)\hspace{.2em}$$ $$x-intercepts: none$$ $$ y-intercepts: none$$


#4:

Solutions:

a)

graphing a circle

#5:

Solutions:

a)

graphing a circle