Parametric equation of ellipse
Categories: coordinate systems pure mathematics
The parametric equation of an ellipse is:
$$ \begin{align} x = a \cos{t}\newline y = b \sin{t} \end{align} $$
Understanding the equations
We know that the equations for a point on the unit circle is:
$$ \begin{align} x = \cos{t}\newline y = \sin{t} \end{align} $$
Multiplying the $x$ formula by $a$ scales the shape in the x direction, so that is the required width (crossing the x axis at $x = a$). In this example, $a > 1$ so the circle is stretched in the x direction:
Multiplying the $y$ formula by $b$ scales the shape in the y direction, so that is the required height (crossing the y axis at $y= b$). In this example, $b < 1$ so the circle is compressed in the y direction:
See also
Join the GraphicMaths Newletter
Sign up using this form to receive an email when new content is added:
Popular tags
angle area cartesian equation chord circle combinations complex polygon cosh cosine cosine rule cube decagon diagonal directrix dodecagon ellipse equilateral triangle exponent exponential exterior angle focus hendecagon heptagon hexagon horizontal hyperbola hyperbolic function interior angle inverse hyperbolic function irregular polygon isosceles trapezium isosceles triangle kite locus major axis minor axis nonagon normal octagon parabola parallelogram parametric equation pentagon perimeter permutations power pythagoras proof quadrilateral radius rectangle regular polygon rhombus root sine rule sinh sloping lines solving equations solving triangles square standard curves star polygon straight line graphs symmetry tangent tanh transformations trapezium triangle vertical