Learning Resources
Lesson
No new concepts are introduced in this lesson; the idea is for you to be able graph relations that are not functions on the TI-83.
It is possible to use your calculator to draw the graph of a circle. However, the calculator can only graph a function and it must be written in the form y = f(x). You should recall that a function assigns only one value of y to each value of x. However, in a circle there are two values of y for each value of x. In short, a circle is not a function. To overcome this, we break the equation into two parts - the top half and bottom half - and graph them separately.
In order to break the equation of a circle into two functions we need to rearrange the equation. We shall concentrate on this skill first. Remember, we are trying to re-write the equation in the form y = (some expression).
Before we begin, recall that every number has two square roots, a positive and a negative one. For example, if x2 = 9, then x = 3 or x = -3 since both numbers when squared give 9. Thus, if 
, then 
or
. The + and - are necessary since the 
symbol means only the principal or positive square root.
Example 1
Solve the following equation for y in terms of x and use this rearranged form to draw its graph using your calculator: x2 + y2 = 36
Solution
To see how to enter this equation into the calculator and draw its graph click here.
Example 2
Solve the following equation for y in terms of x and use this rearranged form to draw its graph using your calculator: 
.
Solution
You should be able to follow the directions from the last example to enter this equation into your calculator. The centre is (2 , -3) and the radius is 
or approximately 6.3 . Use this information to set the window correctly. For example, set the x values 7 above 2 and 7 below 2 (Xmax = 9, Xmin = -5) and the y values 7 above -3 and 7 below -3 (Ymax = 4, Ymin = -10. Do this first, then enter the equation. Zoom square to make it a circle.
To see some of the steps in the procedure for entering the equation of this circle click here.
Activity
Focus Questions p. 261. Complete 35 and 36
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
Answer the following questions about the circle with equation
x2 + y2 - 6x + 10y - 3 = 0.
- Rewrite the equation in standard form.
- Give the coordinates of the centre and radius.
- Rewrite the equation in a form suitable for graphing on your calculator.
- Select values for a suitable "window".
- Sketch the graph on your calculator.
Click here for suggested solutions.