Parametric equations
Categories: coordinate systems pure mathematics
We often define a curve by expression $x$ as a function of $y$:
$$y = f(x)$$
Using parametric equations we define the $x$ and $y$ coordinates of the points on the curve in terms of an independent variable, which we will call $t$:
$$ \begin{align} x = g(t)\newline y = h(t) \end{align} $$
For any value of $t$, a value of $x$ and $y$ can be calculated, and the point $(x, y)$ will lie on the curve.
One way to think of this is to imagine $t$ representing time. As the time changes, the point $(x, y)$ will move, tracing the curve. But this is just an aid to understanding, the parameter $t$ does not necessarily represent time.
In this section we will look at the parametric equations of parabolas and hyperbolas, and also see how to express them as Cartesian equations.
See also
Join the GraphicMaths Newletter
Sign up using this form to receive an email when new content is added:
Popular tags
adder adjacency matrix alu and gate angle area argand diagram binary maths cartesian equation chain rule chord circle cofactor combinations complex polygon complex power complex root cosh cosine cosine rule cpu cube decagon demorgans law derivative determinant diagonal directrix dodecagon ellipse equilateral triangle eulers formula exponent exponential exterior angle first principles flip-flop focus gabriels horn gradient graph hendecagon heptagon hexagon horizontal hyperbola hyperbolic function infinity integration by substitution interior angle inverse hyperbolic function inverse matrix irregular polygon isosceles trapezium isosceles triangle kite koch curve l system locus maclaurin series major axis matrix matrix algebra minor axis nand gate newton raphson method nonagon nor gate normal not gate octagon or gate parabola parallelogram parametric equation pentagon perimeter permutations polar coordinates polynomial power probability probability distribution product rule pythagoras proof quadrilateral radians radius rectangle regular polygon rhombus root set set-reset flip-flop sine sine rule sinh sloping lines solving equations solving triangles square standard curves star polygon straight line graphs surface of revolution symmetry tangent tanh transformations trapezium triangle turtle graphics vertical volume of revolution xnor gate xor gate