Search Results for “ellipse”
Ellipse Incenter Locus
What is the locus of the incenter of the triangle formed by the string in the "two pins and a piece of string" construction of an ellipse?
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.
Polar Point Ellipse
The polar point of a line in an ellipse is a common point to the chords defined by the common tangents through the points on the line. Play with it and the meaning will be clear! (Go to Full Screen if the green points won't drag)
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.
Projectile High Point
Press the play button to fire a projectile in the direction of the arrow. Move the arrow and try again. Notice the high points of the trajectory lie on an ellipse. If the initial velocity of the projectile is v, and gravity is g, what is the equation of the ellipse?
Polar Line
The locus of the intersections of the tangents at the end of chords of an ellipse which pass through a common point is a straight line. A bit of a mouthful, but play with the diagram and it will become clear.
proof without words
A proof that the locus of the center of a circle tangential to two nested circles is an ellipse.
Trammel foci
Altering |AB| and |AC| changes the ellipse. Can you find a relationship between |AB|, AC| and |DE|, the distance between the foci?
