# Elementary Curves

The simplest of all curves are the straight lines. The next in complexity are the second degree or conics curves.

### Non-degenerate Conics

#### Ellipse

x^{2 }/ a^{2}+ y^{2 }/ b^{2}= 1 (1)

where

a, b = intrinsic parameters

#### Circle

Circle, a special ellipse, can be expressed as

x^{2}+ y^{2 }= a^{2}(2)

where

a = radius

#### Hyperbola

x^{2 }/ a^{2}- y^{2 }/ b^{2}= 1 (3)

where

a, b = intrinsic parameters

#### Parabola

y^{2}- 2 l x = 0 (4)

where

l = intrinsic parameter

### Degenerate Conics

#### Parallel Lines

x^{2}- a^{2}= 0 (5)

where

a = half the distance between the parallel lines

#### Intersecting Lines

x^{2 }/ a^{2}- y^{2 }/ b^{2}= 0 (6)

where

tan^{-1}(b/a) = half the angle between the intersecting lines

#### Coincident Lines

x^{2}= 0 (7)

## Related Topics

### • Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

### Area of Intersecting Circles

Calculate area of intersecting circles

### Centroids of Plane Areas

The controid of square, rectangle, circle, semi-circle and right-angled triangle.

### Circle - Equation

The equation for a circle

### Circle - the Chord Lengths when Divided in to Equal Segments

Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.

### Circles - Circumferences and Areas

Circumferences and areas of circles with diameters in inches.

### Circles Outside a Circle

Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.

### Circles within a Rectangle - Calculator

Calculate the maximum number of circles within a rectangle - can be used to calculate the numbers of pipes or wires in a conduit or similar.

### Elementary Surfaces

Ellipsoid, sphere, hyperboloid, cone and more.

### Equal Areas - Circles vs. Squares

Radius and side lengths of equal areas, circles and squares.

### Geometric Shapes - Areas

Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..

### Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.

### Radians vs. Degrees

Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.

### Smaller Circles within a Large Circle - Calculator

Calculate the number of small circles that fits into an outer larger circle - ex. how many pipes or wires fits into a larger pipe or conduit.