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
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.
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?
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?
Parabola Tangent Circumcircle
3 tangents of a parabola form a triangle. Its circumcircle passes through the parabola's focus.
Parabolic Reflector
A parabola reflects rays which are parallel to its axis of symmetry through its focus. What happens when the rays are not parallel to the axis?
Ellipse Reflection Property
The reflection of a ray of light emanating from one focus of an ellipse passes through the other focus. This app uses a zip line to show why.
