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Search Results for “focus”

Focus Directrix Parabola
Try to set the focus and directrix of a parabola so it matches one with a given equation

Tags: parabola, focus, directrix

Caustic curve as focus of parabola
The red curve is f(x) (for -2≤x≤2).  The blue curve is the terms up to the square term of the Taylor series.  A is the vertex of this parabola, B is its focus. The orange curve is the caustic - envelope of the reflection of vertical rays reflected in a mirror aligned with f(x). Observe that the focus of the parabola traces the caustic.

Tags: caustic, Taylor-series, parabola

Projectile Focus
You are shooting a projectile on a sloping field.  Drag the red point to change the angle of the projectile and try and maximize |AB|. Click the button to see the focus of the parabola. What do you notice?

Tags: parabola, projectile, range

By Duncan
Rolling Parabola
If you roll a parabola along the ground, what curve does its focus trace out? It might look like a parabola, but is it?

Tags: parabola, catenary, focus

Parabola Tangent Circumcircle
3 tangents of a parabola form a triangle.  Its circumcircle passes through the parabola's focus.

Tags: parabola, focus, circumcircle

Parabola Directrix
Explore the focus and directrix of a parabola

Tags: parabola, focus, directrix

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

proof without words
A proof that the locus of the center of a circle tangential to two nested circles is an ellipse.

Tags: ellipse, 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

Parabola Subnormal
The subnormal for a given parabola is constant, and closely related to the focal length.

Tags: parabola, focus, conic