A bio-medical device, as shown in the graphic below, generates sound waves at one focus of an ellipse - Leaving Cert DCG - Question A-2 - 2011

The focus of an ellipse lies along the major axis. If the first focus is at (2,1), then the coordinates of the second focus are the same, i.e., (2,1).

To determine points on the curve, use the standard form of an ellipse equation, which can be derived from the vertices and foci. The points can be calculated as follows:

• Points at major axis extremes: (2, 2) and (2, 1)
• Minor axis endpoints can be calculated based on the lengths derived from the vertices. For example, consider points (1, 2) and (3, 2).
• A few calculated points might include (2, 1.5), (2.5, 1.5), (1.5, 2).

The resulting graph should represent the ellipse defined by the given parameters. Make sure to reflect the symmetry about both axes and clearly indicate the vertices and foci.

To identify the point that is 70mm from the focus (F), measure along the major axis (or direction determined) to locate the point. Convert this measurement into corresponding coordinates based on the ellipse's dimensions.

To draw a tangent to the curve at the identified point, utilize the slope derived from the ellipse equation at that point. The tangent line can be sketched using point-slope form of a line, keeping the continuity of the curve in mind.