Search Results for “Ellipses”
Rotating Ellipses with Arcs
Now that you know how two ellipses can rotate such that they are tangent to each other and a third larger ellipse (see this app); the next challenge is to figure out how an arc placed on each ellipse can be constrained (with proportional points along the ellipses) such that each arc always covers half of the ellipse and one endpoint is on the tangent point of the two smaller ellipses.
Rotating Ellipses
Two ellipses rotate within a third such that the two smaller ellipses are always tangent to each other and the larger ellipse. Adjusting the variable X demonstrates this rotation. All three ellipses are constrained only by their implicit equations, and the moving ellipses' equations include functions of X that allow them to rotate. Can you figure out what the equations are (the other constants in the equations are a, b, h, and k)?
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?
Ellipse Generalization
A theorem of Archimedes on a circle can be generalized to ellipses as shown here. CE is a diameter of the ellipse. FG is parallel to the tangent at C. H is the intersection of the tangents at F and C. Observe that EH bisects FG.
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.
Ellipse Equations
This app allows you to practice writing the equation of an ellipse (horizontal and vertical) given a graph. (G-GPE 3)
Alternate Ellipse Construction
This app allows you to experiment with an alternate construction of an ellipse. The tracing of the perpendicular bisector of the segment between a point on a circle and a point in the circle create an elliptical locus. (G-GPE 3)
