Graphing Circles
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1
2EL-9900 Graphing Calculator
Graphing Circles
2
The standard equation of a circle of radius r that is centered at a point (h, k) is (x - h)
+
(y - k)
2
2
. In order to put an equation in standard form so that you can graph in rectangular
= r
mode, it is necessary to solve the equation for y. You therefore need to use the process of
completing the square.
Example
Graph the circles in rectangular mode. Solve the equation for y to put it in the
standard form.
1.
2
2
Graph x
+ y
= 4.
2.
2
2
Graph x
- 2x + y
+ 4y = 2.
Before
There may be differences in the results of calculations and graph plotting depending on the setting.
Starting
Return all settings to the default value and delete all data.
Set the zoom to the decimal window:
A
(
)
ZOOM
7
ENTER
ALPHA
Step & Key Operation
Display
Notes
1
1
Solve the equation for y.
2
2
-
y
= 4 - x
√
√
+ –
Enter y =
4 - x
2
for Y1 (the top
2
y =
4 - x
√
half). Enter y = -
4 - x
2
for Y2.
x
√
n
Y=
—
2
2nd F
4
X/ /T/
-
(
)
A
1
ENTER
2nd F
VARS
ENTER
1
2
This is a circle of radius r ,
View the graph.
-
centered at the origin.
GRAPH
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
2
x
2
- 2x + y
2
+ 4y = 2
Place all variable terms on the
1
-
Solve the equation for y,
left and the constant term on
completing the square.
the right-hand side of the
equation.
2
2
+4 y + 4 = 2 + 4
Complete the square on the
x
-2 x + y
y-term.
x
2
- 2x + (y+2)
2
= 6
Express the terms in y as a
perfect square.
(y+2)
2
= 6 -x
2
+ 2x
Leave only the term involving
y on the left hand side.
y+2 = ±
√
6-x
2
+2x
Take the square root of both
sides.
y = ±
√
2
6-x
+2x -2
Solve for y.
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