# Parametric equation for an ellipse

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## What is the parametric equation of an ellipse?

The parametrization represents an ellipse centered at the origin, albeit tilted with respect to the axes. (You can demonstrate by plotting a few for yourself.) The general form of this ellipse is ## Parametric Equation of the Ellipse

a set of parametric equations for it would be, x =acost y =bsint x = a cos t y = b sin t This set of parametric equations will trace out the ellipse starting at the point (a,0) ( a, 0) and will trace in a counter-clockwise direction

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## Parameterize any Ellipse

Let the ellipse be in the canonical form with parametric equation p → ( t ) = ( a cos ⁡ t , b sin ⁡ t ) {\displaystyle {\vec {p}}(t)=(a\cos t,\,b\sin t)} . The two points c → 1 = p → ( t ) , c → 2 = p → ( t + π 2 ) {\displaystyle {\vec {c}}_{1}={\vec {p}}(t),\ Fast solutions

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