What are Engineering Curves?

Engineering curves are mathematical representations of various shapes and profiles used in engineering design and analysis. These curves often have specific properties or characteristics that make them suitable for particular applications. These curves include ellipse, parabola, hyperbola, cycloids, trochoids, involutes, and spirals.

What are Conic Sections?

Conic sections are formed when a plane intersects with a double cone. There are three types of conics: parabolas, ellipses (including circles,) and hyperbolas

What are Parabolas?

Parabola as a conic section:

A parabola is formed when a plane cuts a double cone is cut at an angle equal to the angle of slant of the side of the cone.

Parabola as a geometric rule:

A parabola is the set of all points in the plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line. Since the distance from each point to the directrix and the focus is always equal the ratio of eccentricity of a parabola is 1:1 or simply 1.

What is an Ellipse?

Ellipse as a conic section

An ellipse is formed when a plane cuts a double cone is cut at an angle of lesser slant than that of the side of the cone but not parallel to the base of the cone.

Ellipse as a geometric rule

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. The distance between any point on the ellipse to the directrix is always larger than the distance to the focus. Therefore, the ratio of eccentricity of an ellipse is always less than 1.

What is a Hyperbola?

Hyperbola as a conic section

An ellipse is formed when a plane cuts a double cone is cut at an angle of greater slant than that of the side of the cone. Both Cones are intersected by the plane. 

Hyperbola as a geometric rule:

A hyperbola is the locus of a point traced out such that the distance between the point and the directrix (d1) and the distance between the point and the focus (d2) is at a constant ratio. D2 is always greater than d2. The ratio of eccentricity of hyperbola is always more than 1 but less than 2.