Elliptical Curves v1

Subject

Elliptical curves describe the path of orbiting objects & trajectories and sections through a cone (conic). See Laws of Motion for a full analysis.

Ellipse: An ellipse is the shape of a curve generated by a straight/flat cut through a single circular cone above its base. It is also the shape of the natural path of an orbiting body (e.g. a planet).

Hyperbola: An hyperbola is the shape of the opposing curves generated by a straight/flat cut through two cones placed tip-to-tip parallel to their axes. It is also the curvature of light around a large gravitational body like a star and the path of subatomic particles repulsed by a nucleus.

Parabola: A parabola is the shape of a curve generated by a straight/flat cut through a single circular cone parallel to its slope. It is also the path of a projectile falling to the ground under the influence of gravity.

Ellipses determines the dimensional properties of the three elliptical curves; ellipse, hyperbola and parabola.

In addition to the shape controlling parameters of these curves, the ellipse calculator also determines arc lengths & areas and provides a co-ordinate listing for the curve between 'y=0' and 'y' maximum

For help using this calculator see Technical Help

The ellipse Calculator - Options

Ellipse

This option calculates the properties of one quarter of a full ellipse, that can be replicated for any other quarter. Ellipses will also calculate the 'y' co-ordinate and radius at the x-co-ordinate entered along with the arc length from x=0.

You enter:	and ellipse calculator will provide:
x-coordinate Half width Half height Number of co-ordinates	y-coordinate Eccentricity Parameter Focal distance Distance from focus₁ to point (P) Distance from focus₂ to point (P) Radius @ x Arc length Area co-ordinate list

Hyperbola

This option calculates the properties of one half of a full hyperbola, that can be replicated for the other half. Ellipses will also calculate the 'y' co-ordinate and radius at the x-co-ordinate entered along with the arc length from x=0.

You enter:	and ellipse calculator will provide:
x-coordinate Distance to vertex Parameter Number of co-ordinates	y-coordinate Eccentricity x-shift of vertex Focal distance Distance from focus₁ to point (P) Distance from focus₂ to point (P) Radius @ x Arc length Area co-ordinate list

Parabola

This option calculates the properties of one half of a full parabola, that can be replicated for the other half. Ellipses will also calculate the 'y' co-ordinate and radius at the x-co-ordinate entered along with the arc length from x=0.

You enter:	and ellipse calculator will provide:
x-coordinate Parameter Number of co-ordinates	y-coordinate Eccentricity Hypotenuse to parameter Focal distance Distance from focus to point (P) Radius @ x Arc length Area co-ordinate list

Check minimum system requirements