Foci_on_ellipse

Focal points on an ellipse

Consider an ellipse c with center M and axes MR, MI. Then from a point L on the ellipse draw a parallel to an axis, e = (LT) say, parallel to MR. Draw the line RW, tangent to c and parallel to the axis MI. Define also the ellipse (d) with foci at L, T and passing through V. As L moves on the ellipse (c) (CTRL+2, pick-move L), the ellipse (d) changes its shape from the circle (QW) to the (degenerate) segment (RS). Besides the points X of ellipse (d) have the following property: Draw the line XZ, parallel to RV and define the intersection points of this line with line MR (Y) and with circle (QW) (Z). Then the length-ratio XY/XZ is constant on (d) and independent of the position of X on (d).
This property is related to the figure Ellipse_Construction2.html .

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