The latus rectum is a chord through a focus, perpendicular to the main axis. Its length measures how “wide” a conic is at the focus and appears in orbital mechanics (the semi-latus rectum p sets the size of an orbit).
How to use the Latus Rectum Calculator
- Shape
- A
- B
- C
- Semi-major axis a
- Semi-minor axis b
- Centre h
- Centre k
Results update as you type, and everything is calculated in your browser.
How it works
For a parabola the focus lies 1/(4A) from the vertex and the latus rectum is 4 times that distance. For an ellipse or hyperbola with semi-axes a and b, the half-length b²/a is the semi-latus rectum.
Inputs explained
| Field | What to enter |
|---|---|
| Shape | Choose one: Parabola y = Ax² + Bx + C, Ellipse (horizontal), Hyperbola (horizontal) |
| A | A number |
| B | A number |
| C | A number |
| Semi-major axis a | A number |
| Semi-minor axis b | A number |
| Centre h | A number |
| Centre k | A number |
Example values
How the main result changes when A changes and everything else stays at the example values above:
| A | Latus rectum length |
|---|---|
| 0.125 | 8 |
| 0.1875 | 5.3333 |
| 0.25 | 4 |
| 0.3125 | 3.2 |
| 0.375 | 2.6667 |
| 0.5 | 2 |
Formula
Parabola y = Ax² + Bx + C: length = 1/|A|
Ellipse / hyperbola: length = 2b²/a, foci at h ± c with c = √(a² ∓ b²)
Worked example
Inputs — Shape: Parabola y = Ax² + Bx + C; A: 0.25; B: -1; C: 3.
Results — Latus rectum length = 4; Focus – x = 2; Focus – y = 3; Endpoint 1 – x = 0; Endpoint 1 – y = 3; Endpoint 2 – x = 4; Endpoint 2 – y = 3.
Key terms
- Latus rectum
- The focal chord perpendicular to the axis of a conic.
Frequently asked questions
What is the latus rectum of y² = 4ax?
4a.
What is the semi-latus rectum?
Half the latus rectum; for orbits it is p = b²/a.
Does a circle have a latus rectum?
Yes – it is the diameter (2r), since a = b = r.
Why does the ellipse use a² − b² and the hyperbola a² + b²?
Those give the focal distance c in each case.