Search Results for “hyperbola”
Hyperbola Generalization
A theorem of Archimedes on a circle can be generalized to a hyperbola as shown here. CE is a diameter of the hyperbola. FG is parallel to the tangent at C. H is the intersection of the tangents at F and C. Observe that EH bisects FG.
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?
Hyperbola Equations
This app allows you to practice writing the equation of a hyperbola (horizontal and vertical) given a graph. (G-GPE 3)
Alternate Hyperbola Construction
This app allows you to experiment with an alternate construction of a hyperbola. The tracing of the perpendicular bisector of the segment between a point on a circle and a point outside the circle create a hyperbolic locus. (G-GPE 3)
Hyperbola Definition
This app allows you to experiment with the definition of a hyperbola as the set of points in which the difference of the distances from two fixed points is a constant. (G-GPE 3)
Hyperbola Polar Line
The polar line is the locus of the intersections of tangent lines at the ends of chords of teh parabola through a fixed point. Turns out to be conceptually important - not just a curiosity.
Rotating Cube
I saw a demo where a foam cube had a knitting needle inserted along the long diagonal, and was rotated by spinning the needle between the palms of the hands. The sides of the cube formed a curve... in fact a portion of a hyperbola, as this video illustrates.
