To draw a straight line tangent to two given ellipses.

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How can I draw a a straight line that touches two ellipses? There are, like for two circles, 4 different solutions. I am not interested in the analytical solution, but in the geometrical drawing, although no matter if conics appear. Thanks.

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You can load the file here into GeoGebra and look in the Construction Protocol to see how the tangents are calculated (in terms of the coefficients of the equation of the conics) https://help.geogebra.org/topic/tangent-to-ellipse

In short:

  • matrix calculation
  • construct a hyperbola
  • Intersect the hyperbola with one ellipse
  • The tangents are then the polar lines of the intersection points

Dynamic Example (drag the points) https://www.geogebra.org/m/Yr9Jfinu

Credit: https://www.geogebra.org/u/mathmagic