## Diameters of an ellipse, after Apollonius
Check the boxes to see vertices, diameters, and chords. Then see an equation for the curve in a coordinate system determined by the tangent at point D, with origin a movable point J.
Move the point H to see that the equation is satisfied by all points on the ellipse. (You may want to check the calculation on a calculator---usually the numbers are awkward to work with.)
Move point J to change the origin of the coordinate system. To move the origin to exactly the point of tangency, type J=D in the input bar. To move the origin to exactly the center of the ellipse, type J=I in the input bar.
Move the point of tangency, D, on the parabola to change the coordinate system.
To change the shape of the ellipse, move the foci, A and B, or the determining point C on the ellipse.
For a given shape of ellipse, how can you get a coordinate system where the axes are perpendicular?
Susan Addington, Created with GeoGebra |