Graphing Circles - Sharp EL9600C - Graphing Calculator Handbook

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
= r
rectangular 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.
Graph x 2 2
+ y
2.
2
Graph x - 2x + y
Before There may be differences in the results of calculations and graph plotting depending on the setting.
Start
Return all settings to the default value or to delete all data.
Set the zoom to the decimal window:
Step & Key Operation
(When using EL-9600)
*Use either pen touch or cursor to operate.
1
1
Solve the equation for y.
-
Enter y = 4 - x
half). Enter y = - 4 - x
Y=
2nd F
-
( )
ENTER VARS
*
1
2
- View the graph.
GRAPH
2
1
-
Solve the equation for y,
completing the square.
10-2
= 4.
2
+ 4y = 2.
A
ZOOM
*
2
for Y1 (the top
2
for Y2.
n
4 — x 2
X/ /T/
A 1
ENTER
* *
2
x
2
x - 2 x + y
2
x
(y+2)
y+2 =
y =
EL-9600/9400 Graphing Calculator
( )
ENTER ALPHA 7
* *
Display
(When using EL-9600)
2
y
y =
This is a circle of radius r ,
centered at the origin.
2
- 2x + y + 4y = 2 Place all variable terms on the
left and the constant term on
the right-hand side of the
equation.
2
+4y + 4= 2+4 Complete the square on the
y-term.
2
- 2x + (y+2) = 6 Express the terms in y as a
perfect square.
2 2
= 6 -x + 2x Leave only the term involving
y on the left hand side.
2
6-x +2x Take the square root of both
sides.
2
6-x +2x -2
Solve for y.
2
+
Notes
2
= 4 - x
+ –
2
4 - x