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The ellipse tool displays a movable ellipse or circle on the graph view, along with other points and lines of interest. (See below:)

 Cursor for ellipse mode: Cursor for circle mode:

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:)

 Drag on the title bar at the top of the ellipse tool dialog box to move it. Check the 'Foci' check box to display the ellipse foci on the graph view. Check the 'Directrices' check box to display the ellipse directrices on the graph view. Check the 'Trace' check box to trace the centre of the ellipse along a function curve.
 Check the 'Snap to grid' option to locate the centre of the ellipse at the corner of grid snap rectangles. Click the 'Cancel' button to stop using the ellipse tool.

Press the space bar on the keyboard to plot graphs of:

 the ellipse as a parametric function.

The parametric form of the ellipse equations are:

Major axis horizontal: x = acosT + h, y = bsinT + k
Major axis vertical:
x = bcosT + h, y = asinT + k

 the foci of the ellipse if the 'foci' check box is checked. the directrices of the ellipse if the 'directrices' check box is checked.

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.

 Drag the mouse horizontally to change the width of the ellipse. Drag the mouse vertically to change the height of the ellipse. For fine adjustment, hold down a Shift key as well.

Circle mode:

The general equation for circles can be written as:

(x - h)² + (y - k)² = a²

Where:

 (h,k) is the centre of the circle. 'a' is the radius of the circle. The circumference of the circle is given by: 2pr The area of the circle is given by: pr²

With the 'circle' check box checked the ellipse tool is in 'circle mode' and this dialog box displays circle equations and values. (See below:)

 Drag on the title bar at the top of the circle tool dialog box to move it. Check the 'Centre' check box to display the centre of the circle on the graph view. Check the 'Trace' check box to trace the centre of the circle along a function curve. Check the 'Snap to grid' option to locate the centre of the circle at the corner of grid snap rectangles.
 Click the 'Cancel' button to stop using the circle tool.

Press the space bar on the keyboard to plot graphs of:

 the circle as a parametric function. the centre of the circle if the 'centre' check box is checked.

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.