Circle Stuff

The equation of a circle and the properties of the circle. The equation used is the standard equation that has the form: (x - h)2 + (y - k)2 = r2 where h and k are the x- and y-coordinates of the center of the circle and r is the radius. The exploration is carried out by changing the parameters h, k and r included in the above 1. h and k to zero and parameter r to 1. Check that the circle shown has the center at (0,0) and radius equal to 1. 3. set r to zero and parameters h and k to different values, the graph of the circle is a point, Explain.(Hint:Solve the equation (x - h)2 + (y - k)2 = 0 4 - Keep r equal to 1 and shift the circle by changing h and k. Check that the center of the circle is at (h , k). 5 - Keep h and k constant and change r. Check that the circle has radius r. 6 - Set h, k and r to 1. The circle has one point of intersection with the x-axis and one point of intersection with the y-axis. These are called the x and y intercepts. Find these points analytically using the equation of the circle. (x - h)2 + (y - k)2 = r2 (Hint: To find the x-intercepts set y = 0 in the equation and solve for x. To find the y-intercepts set x = 0 in the equation and solve for y.) 7- Set r to 2 and h to a certain value. Change k from -1.8 to 1.8 (|h| less than r). How many x-intercepts are there? Set k to 2 (the radius), How many x-intercepts are there? Set k to -2, how many x-intercepts are there? Set k to values greater than 2 (the radius), how many x-intercepts are there? Set k to values smaller than -2, how many x-intercepts are there? Explain analytically. 8- Try the same exploration as in 7 above with the y-intercepts by changing the value of h. 9- Exercise: Find (analytically) values of h, k and r such that the circle associated with these values has no x or y-intercepts. Check your answer graphically. From the website: http://www.analyzemath.com/CircleEq/CircleEq.html