Another Tricky Locus

Calculus Level 5

Ellipses are inscribed in a fixed convex quadrilateral with all sides of different lengths.

The centers of the ellipses lie on which of the given curves?

An ellipse A point A pair of straight lines None of the given options A circle A straight line

Digvijay Singh by Digvijay Singh , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Hosam Hajjir
Jul 17, 2019

Here's an animation of a sequence of inscribed ellipses in a certain quadrilateral.

2 Helpful 0 Interesting 2 Brilliant 0 Confused

Great graphic. Thanks for visualizing it.

On a totally different note: Could you please provide a picture of envelope of ellipses (with fixed semi major and semi minor axes) that are tangent to the coordinate axes in the first quadrant?

I can't seem to visualize it.

Digvijay Singh - 1 year, 10 months ago

Log in to reply

I wasn't able to find the envelope of the family of ellipses that you asked for. I did however manage to obtain a picture of superimposed ellipses that belong to this class by varying the angle of the major axis from 0 to 180. But I don't know how to upload that graphic into this answer box.

Hosam Hajjir - 1 year, 10 months ago
Jon Haussmann
Jul 19, 2019

See http://www2.washjeff.edu/users/mwoltermann/Dorrie/49.pdf .

0 Helpful 1 Interesting 1 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...