Parabola Calculator
Focus, directrix, vertex and latus rectum of a parabola.
Reviewed by James Whitfield · How we check our maths
Your values
ⓘ Live results
Results
- Vertex
- (2, -1)
- Focus
- (2, -0.5)
- Directrix
- y = -1.5
- Focal length
- 0.5
- Latus rectum length
- 2
- Opens
- Upward
- Axis of symmetry
- x = 2
Quick answer
For y = ax² + bx + c the vertex is at x = −b/2a and the focus sits 1 ÷ (4a) above it, with the directrix the same distance below.
The formula
focal length p = 1 ÷ (4a)
Worked example
Worked example
Using the values the calculator loads with.
Inputs
- a0.5
- b-2
- c1
Result
- Vertex(2, -1)
- Focus(2, -0.5)
- Directrixy = -1.5
- Focal length0.5
- Latus rectum length2
- OpensUpward
How to use the Parabola Calculator
- 1Enter the coefficients of y = ax² + bx + c.
- 2Read the vertex, then the focus and directrix.
- 3Use the latus rectum width to sketch the curve accurately through three points.
Frequently asked questions
Why does a satellite dish use a parabola?
Every ray parallel to the axis reflects through the focus, so the receiver sits exactly at the focal point.
What is the latus rectum?
The chord through the focus parallel to the directrix; its length is 1 ÷ |a| and it fixes how wide the curve opens.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error