Focus-Directrix Construction of Ellipse and Hyperbola
Focus-directrix definition of an ellipse
The set of points equidistant from a circle and a point inside the circle.
Note: distance to a circle is to the closest point on the circle: along a radius, which is perpendicular to a tangent. The two equal sides of the isosceles triangle show the equal distances.
This is the paper-folding construction of an ellipse. The tangent line is the fold line.
If the point is outside the circle, you get a hyperbola.
To see many tangent/fold lines, drag D around the circle or click the “Play” button at lower left. To remove traces, drag the background.