Learning Resources

Lesson

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 manipulate 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 -3 since both numbers when squared give 9. Thus, if x² = n,  then x  = or x  = - . 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:   (x - 2)² + (y + 3)² = 40

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 and below 2 (Xmax = 9, Xmin = -5) and the y values 7 above and 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

1. Read through the examples in Focus I on pages 260 & 261 in your text.
2. Complete the Focus Questions 35 & 36 on page 261.

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.

Test Yourself

Answer the following questions about the circle with equation x² + y² - 6x + 10y - 3 = 0.

1. Rewrite the equation in standard form.
2. Give the coordinates of the centre and radius.
3. Rewrite the equation in a form suitable for graphing on your calculator.
4. Select values for a suitable "window".
5. Sketch the graph on your calculator.

Solution