There are different Engineering Curves:
Cone is a surface generated by making a straight line keeping one of its end fixed and other end making a closed curve. 

Conics: The locus of point moves in a plane in such a way that the ratio of its distance from a fixed point (focus) to a fixed straight line (Directrix) is always constant. PF/PM = Const 

Ellipse is the locus of a point which moves in a plane so that the ratio of its distance from a fixed point (focus) and a fixed straight line (Directrix) is a constant and less than 1. PF/PM < 1 

Parabola is the locus of a point, which moves in a plane so that its distance from a fixed point (focus) and a fixed straight line (directrix) are always equal. PF/PM = 1 

Hyperbola is the locus of a point which moves in a plane so that the ratio of its distances from a fixed point (focus) and a fixed straight line (directrix) is constant and greater than one. 

Cycloidal group of curves: When one curve rolls over another curve without slipping or sliding, the path of any point of the rolling curve is called as Roulette. When the rolling curve is a circle and the curve on which it rolls is a straight line or a circle, we get cycloidal groups of a curve. 

A cycloid is a locus of a point on the circumference of a rolling circle (generator), which rolls without slipping or sliding along a fixed straight line or a directing line. 

Epicycloid is a locus of a point on the circumference of a rolling circle (generator), which rolls without slipping or sliding outside another circle called directing circle. 

Hypocycloid is a locus of a point (P) on the circumference of a rolling circle (generator), which rolls without slipping or sliding inside another circle called directing circle. 

A trochoid is a locus of a point inside/outside the circumference of a rolling circle, which rolls without slipping or sliding along a fixed straight line or a fixed circle. 