The ellipse tool displays a movable ellipse or circle on the graph view, along with other points and lines of interest. (See below:)
The ellipse tool also displays equations, coordinates and calculated values, and plots the curves, lines and points directly. Select the ellipse tool by clicking the button on the graph tools tool bar, or by selecting the 'Ellipse' command from the 'Tools' menu. When selected, the ellipse tool dialog box is displayed (See below:). Checking the 'circle' check box changes the ellipse tool into 'circle mode'. When the 'circle' check box is not checked, the ellipse tool is in 'ellipse mode'. ## Ellipse mode:An ellipse is an oval shape with one dimension (width or height) bigger than the other. (Stated mathematically, an ellipse is the path traced out by a point such that the sum of the distances from the point to two other fixed points is a constant. The fixed points are called the 'foci' of the ellipse.) The bigger dimension of an ellipse is called the 'major axis', while the smaller dimension is the 'minor axis'. Ellipses created by the ellipse tool can have the major axis in the 'x' direction (call this a 'type 1' ellipse), or the 'y' direction (call that a 'type 2' ellipse). The equations for type 1 and 2 ellipses are as follows: Note particularly how the values in the equations relate to the ellipses in each case. With the 'circle' check box not checked the ellipse tool is in 'ellipse mode' and this dialog box displays ellipse equations and values. (See below:)
## Press the space bar on the keyboard to plot graphs of:
The parametric form of the ellipse equations are: Major
axis horizontal:
x
= acosT
+ h,
y
= bsinT
+ k
## Changing the shape of the ellipse:With the ellipse tool displaying the ellipse on the graph view, click and hold the left mouse button while moving the mouse.
## Circle mode:The general equation for circles can be written as: (x - h)² + (y - k)² = a² Where:
With the 'circle' check box checked the ellipse tool is in 'circle mode' and this dialog box displays circle equations and values. (See below:)
## Press the space bar on the keyboard to plot graphs of:
## Changing the radius of the circle:With the ellipse tool in circle mode displaying a circle on the graph view, click and hold the left mouse button while moving the mouse left or right. This will change the radius of the circle. For fine adjustment, hold down a Shift key as well. |