1. Curves & circles

2. Write down a possible equation that this could represent y = 6 – 3x or y = -3x + 6

3. Write down a possible equation that this could represent y = x 2 + 3

4. Write down a possible equation that this could represent y = 1 / x 2

5. Write down a possible equation that this could represent y = 2x - 4

6. Write down a possible equation that this could represent y = x 3

7. Write down a possible equation that this could represent y = 1 / x

8. Write down a possible equation that this could represent y = 2x 2

9. Write down a possible equation that this could represent y = (x + 3) 2

10. Write down a possible equation that this could represent y = ln x

11. Write down a possible equation that this could represent y 2 + x 2 = 25

12. Write down a possible equation that this could represent y = -(x + 3) 2 + 3

13. What is the relationship between y=x, y=e^x and y = ln(x)

14. Draw a 4 quadrant axis from -10 to 10. Plot the 2 above equations by: Calculating the value of y when x = 0 Calculating the value of x when y = 0 HINT … have you plotted 2 or 4 coordinates? 1.What have you noticed…? 2.How can you draw on circles without plotting points?

15. What is the general formula for the equation of a circle?

16. Examples Find the equation of a circle where the centre is (4,3) and the radius 4 A line joining (0,-3) and (0,5) is a chord to a circle. The midpoint of the chord is y=1. Sketch the possible options for the circle including identifying their centres. The radius of the circle is 5

17. Examples Find the equation of a circle where the centre is (4,3) and the radius 4

18. A line joining (0,-3) and (0,5) is a chord to a circle. The midpoint of the chord is y=1. Sketch the possible options for the circle including identifying their centres.

22. Additional Example Find the equation of a circle that has centre (3,-2) and passes through (0,2) (3, -2) (0, 2) Pg 66 – ex 2e