A curve where the difference between distances to two foci stays the same
If an ellipse is a curve where the "sum" of distances to two foci is constant, a hyperbola is a curve where the "difference" between distances to two foci is constant. Move the point with the sliders to confirm this definition, then explore the two asymptotes the hyperbola keeps approaching but never quite touches.
a is the distance to the vertex, and c is the distance to the focus (c > a). Move the point on the right branch with the slider, and check whether the difference between its distance to Fâ and its distance to Fâ always stays equal to 2a.
a (distance to the vertex)3
c (distance to the focus)5
Position of the point (t)0.5
A hyperbola gets endlessly closer to two lines through the origin (the asymptotes) y = Âą(b/a)x, but never touches them. Change a and b and see how the slope of the asymptotes changes.