SPECIALIST MATHEMATICS UNIT 3: COORDINATE GEOMETRY - CIRCLES

‘Essential Specialist Mathematics’ text book (3rd edition) was used for the selection of questions below. TI Nspire CAS OS 3.2.1

Exercise 1F

Question 3 f.

Sketch the graph of the following:

We may want to change from the general form to centre-radius form first:

or

To draw it, make y the subject

Use the list {1,-1} expression for the sign to draw and to define it as let say f.

The calculator will find the y-intercepts by using substitution. However, it will not find x-intercepts by solving. Note that f is the relationship, not the function. You need to define a new expression here, f1, being the lower semi-circle and then solve f1 for zero. See the screens below.

Menu: 3: Graph Entry 3: Circle, there are two options. You can enter the equation in general form as 2: or in centre-radius form as 1:
Use the list {1,-1} expression for the sign to draw the circle when using option 1: above.
Note: by default there is a minus sign in option 1 so you need to enter , which is a little bit tricky. /
You can determine the centre and radius by Menu 6: Analyze Graph 8: Analyze Conics 1: Centre and 7: Radius
/
Define the circle as f1(x). Find y-intercepts.
/
Define the lower semi-circle as f2(x). Solve for zero to find the x-intercepts. Mode in Exact if exact answers required.

Question 7 Find the equation of the circle which passes through (3, 1), (8,2) and (2,6).

Use the form
to create 3 simultaneous equations by substituting the coordinates of the points:
/

Then use your calculator to solve and substitute the values back into to obtain the equation of the circle

You may wish to draw check that the 3 given points actually lay on the circle.

Interpret the answers given by the calculator.

Question 9b. Find the coordinates of the points of intersection of the circle with equation and the line with equation

Using the calculator:

The solutions are and

You can enter equation of the circle and then change graph entry to 1: Function to enter the straight line. Both will appear in the same screen. Then you can find the points of intersection (numerical values only) in the screen.

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