 Manufacturer CalQlata Limited

# 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.

## 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 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
Price: £15.75
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