Resources for Parametric Form
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Questions
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Parametric Form Theory
NSW Y11 Maths - Extension 1 Functions Parametric Form
Videos
Videos relating to Parametric Form.
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Parametric Form - Video - Parametric Equations in 7 minutes
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Theory
\(x = f(t),\,y = g(t)\,\,{\rm{or }}x = f(\theta ),\,y = g(\theta )\) are parametric forms and are another technique in representing a function.
For example, the parabola \(y = \dfrac{1}{4}{x^2}\) in the cartesian form can be represented in the parametric form as \(x = 2t,\,y = {t^2}\) and by substituting values for \(t\) the parabola can be graphed.
Another example is the circle \({x^2} + {y^2} = 1\) in the cartesian form can be represented in the parametric form by \(x = \cos \theta ,\,\,y = \sin \theta \).
Syllabus Reference
NSW Syllabus Reference: ME-F1.4 Parametric form of a function or relation. This will require student to
- understand the concept of parametric representation and examine lines, parabolas and circles expressed in parametric form
- understand that linear and quadratic functions, and circles can be expressed in either parametric form or Cartesian form
- convert linear and quadratic functions, and circles from parametric form to Cartesian form and vice versa
- sketch linear and quadratic functions, and circles expressed in parametric form