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Search Results for “foci”

By Phil Todd
Trammel foci
Altering |AB| and |AC| changes the ellipse. Can you find a relationship between |AB|, AC| and |DE|, the distance between the foci?

Tags: ellipse, foci, trammel, principal-axes

By Phil Todd
Circle Envelope
The ellipse has foci A and B. The family of circles whose center C lies on an ellipse and which pass through a  fixed point D defines an envelope curve. (Press Show). What does the envelope look like when D lies on one of the foci of the ellipse.

Tags: ellipse, envelope, circle, isotomic

By Phil Todd
Ellipse Isotomic
The ellipse isotomic generated by point D is teh locus of the reflection of D in the tangents to the ellipse. What shape is the isotomic when D lies on one of the foci of the ellipse? Why?

Tags: isotomic, ellipse

By Phil Todd
A Locus Problem
The locus of the Center of Gravity of the triangle OBA' is shown.  (B is the intersection of the line OA with the inner circle, A' is the image of A under reflection in the x-axis) Looks like an ellipse.  Is it? If so, what are the foci in terms of the circle radii.

Tags: ellipse, circle

By Phil Todd
Circle Envelope (Hyperbola)
The hyperbola has foci A and B. The family of circles whose center C lies on the hyperbola and which pass through the fixed point D defines an envelope curve. What does this envelope look like when D lies on A or B?

Tags: hyperbola, envelope, isotomic

By Phil Todd
Ellipse as locus of circle center
Take two overlapping circles.  Examine the locus of the center of the circles tangential to both. It seems to be an ellipse with foci at the centers of the two circles. Prove it.

Tags: ellipse, conic, focus

By Duncan
Focal Triangle
Create a triangle which has 3 points on the circumference of an ellipse, and two sides passing through the foci.  Look at 2 curves formed by the third side: the locus of its center and its envelope.  One is an ellipse, the other is not.

Tags: ellipse, focus

By Phil Todd
Ellipse Reflection Property
One definition of an ellipse is as the locus of points the sum of whose distance from two fixed points (the foci) is constant. This gives you a way to draw the ellipse with two pins and a piece of string. Here we relate that definition to the focal property: that light emanating from one focus reflects to the other focus.

Tags: ellipse, reflection


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