Parabola example

Martin McBride, 2020-09-12
Tags parametric equation parabola
Categories coordinate systems pure mathematics

A parabola is a curve with the parametric equations:

$$ \begin{align} x = a t^2\newline y = 2 a t \end{align} $$

Where $a$ is a positive constant, and $t$ is the independent variable.

We can plot this curve by calculating the values of $x$ and $y$ for various values of $t$, and drawing a smooth curve through them.

Curve for a = 1

Assuming $a = 1$, the parametric equations simplify to:

$$ \begin{align} x = t^2\newline y = 2 t \end{align} $$

The values are shown in the following table, for $t$ in the range -3 to +3:

t	x	y
-3	9	-6
-2	4	-4
-1	1	-2
0	0	0
1	1	2
2	4	4
3	9	6

Here are the points plotted on a graph:

The curve can be drawn by plotting the points and drawing a smooth line through them:

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Coordinate systems

1. Introduction
2. Parametric equations
3. - Parabola example
4. - Hyperbola example
5. Parabolas
6. - Cartesian equation
7. - Focus and directrix
8. - Effect of 'a'
9. Hyperbolas
10. - Cartesian equation
11. Ellipses
12. - Parametric equation
13. - Cartesian equation

See also

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2. Recent articles
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Links

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2. schoolcoders.com