Elliptical Curves
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 tiptotip 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.
Calculator
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 coordinate 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' coordinate and radius at the xcoordinate entered along with the arc length from x=0.
You enter: 
and ellipse calculator will provide: 


ycoordinate

Eccentricity

Parameter

Focal distance

Distance from focus₁ to point (P)

Distance from focus₂ to point (P)

Radius @ x

Arc length

Area

coordinate 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' coordinate and radius at the xcoordinate entered along with the arc length from x=0.
You enter: 
and ellipse calculator will provide: 


ycoordinate

Eccentricity

xshift of vertex

Focal distance

Distance from focus₁ to point (P)

Distance from focus₂ to point (P)

Radius @ x

Arc length

Area

coordinate 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' coordinate and radius at the xcoordinate entered along with the arc length from x=0.
You enter: 
and ellipse calculator will provide: 


ycoordinate

Eccentricity

Hypotenuse to parameter

Focal distance

Distance from focus to point (P)

Radius @ x

Arc length

Area

coordinate list

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