Graphing Circles - Sharp EL-9900 Handbook Vol. 1 Operation Manual

Graphing Circles

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
2.
2
Graph x - 2x + y
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:
Step & Key Operation
1
1
Solve the equation for y.
-
Enter y = 4 - x
half). Enter y = - 4 - x
Y=
2nd F
-
( )
ENTER 2nd F
1
2
View the graph.
-
GRAPH
2
1
-
Solve the equation for y,
completing the square.
12-2
= 4.
2
+ 4y = 2.
ZOOM
2 for Y1 (the top
2 for Y2.
x
n
— 2
4 X/ /T/
A
1
VARS ENTER
x 2
2
x -2 x + y
x 2
(y+2)
y+2 =
y =
EL-9900 Graphing Calculator
(
A
ENTER ALPHA
Display
2
y
y =
This is a circle of radius r ,
centered at the origin.
- 2x + y 2 + 4y = 2 Place all variable terms on the
left and the constant term on
the right-hand side of the
equation.
2 +4 y + 4 = 2 + 4 Complete the square on the
y-term.
- 2x + (y+2) 2 = 6 Express the terms in y as a
perfect square.
2 = 6 -x 2 + 2x Leave only the term involving
y on the left hand side.
6-x 2 +2x Take the square root of both
sides.
2
6-x +2x -2
Solve for y.
2
+
)
7
Notes
2
= 4 - x
+ –
2
4 - x