Sharp EL-9400, EL-9600c Graphing Circles, EL-9650/9600c/9450/9400 Graphing Calculator, Example

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Circles

The standard equation of a circle of radius r that is centered at a point (h, k) is (x - h) 2 + (y - k) 2 = r 2. In order to put an equation in standard form so that you can graph in 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 + y 2 = 4.

2. Graph x 2 - 2x + y 2 + 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:

ZOOM A * (

ENTER ALPHA

*)

7*

Step & Key Operation	Display	Notes
(When using EL-9650/9600c)	(When using EL-9650/9600c)
*Use either pen touch or cursor to operate.

1-1

Solve the equation for y.

Enter y =

√

4

- x

2

for Y1 (the top

half). Enter y = -√

4 - x 2

for Y2.

Y=

2nd F

√

4

—

X/ /T/n

x 2

*

ENTER

(-)

VARS

A

*

ENTER

1

*

y 2 = 4 - x 2 y = +–√4 - x 2

1-2View the graph.

GRAPH

2-1Solve the equation for y, completing the square.

This is a circle of radius r , centered at the origin.

x 2 - 2x + y 2 + 4y = 2				Place all variable terms on the
				left and the constant term on
				the right-hand side of the
				equation.
x 2 - 2 x+y 2 + 4 y+ 4 = 2 + 4				Complete the square on the
				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 = ± √				Take the square root of both
		6-x 2+2x
y = ± √				sides.
			-2
	6-x 2+2x			Solve for y.

10-2