Instructions.

The surface is the double cone \(x^2 + y^2 = z^2\text{,}\) cut by the plane \(z = m\,y + c\text{.}\) Use the buttons to jump to the three cases, or drag the “tilt” slider yourself and watch the red curve change from an ellipse (\(m \lt 1\text{,}\) plane shallower than the slant) to a parabola (\(m = 1\text{,}\) plane parallel to the slant) to a hyperbola (\(m \gt 1\text{,}\) plane steep enough to cut both nappes). The “offset” slider moves the plane up and down; try setting \(c = 0\) so the plane passes through the apex and the section degenerates to a point, one line, or a pair of crossing lines. Drag the figure to view it from a different angle, or press the “Rotate” button to spin it automatically.