
This is an HTML5 applet to explore 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} = r^{ 2}
where h and k are the x and ycoordinates 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 equation. Follow the steps in the tutorial below. If you wish to go through a tutorial on finding equations of circles, center, radius and other questions Go here.
Similar tutorials on the ellipse , parabola and the hyperbola can be found in this site.
Interactive Tutorials
Use an HTML5 Applet for Interactive Exploration
1  click on the button above "draw" to start. Use the buttons + and  in the left panel to zoom in and out.
2  Use the sliders(for chrome and Safari) and/or input boxes to set parameters 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  Special case: Use the sliders and/or input boxes to 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 xaxis and one point of intersection with the yaxis. These are called the x and y intercepts. Find these points analytically using the equation of the circle.
(x  h)^{ 2} + (y  k)^{ 2} = r^{ 2}
(Hint: To find the $x$intercepts set y = 0 in the equation and solve for x. To find the yintercepts 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 < r). How many xintercepts are there? Set k to 2 (the radius), How many xintercepts are there? Set k to 2, how many xintercepts are there? Set k to values greater than 2 (the radius), how many xintercepts are there? Set k to values smaller than 2, how many xintercepts are there? Explain analytically.
8 Try the same exploration as in 7 above with the yintercepts 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 yintercepts. Check your answer graphically.
More links related to the equation of circle
Analytical Tutorials

