Example: Parametric equation of a circle

The following example is used.

\text{A curve has parametric equations } \\ \\ x= \sin t-2 \text{, }y= \cos t+1 \text{ where }t\in \mathbb{R} \text{, } \\ \\ \text{Show that the Cartesian equation of the curve} \\ \\ \text{is a circle and sketch the curve.}

Example: Parametric equation of a parabola

The following example is used.

\text{A curve has parametric equations } \\ \\ x= \cot t+1 \text{, }y= \mathrm{cosec}^2 t-4 \text{ where }0<t< \pi \text{, } \\ \\ \text{Show that the Cartesian equation of the curve} \\ \\ \text{is a parabola and sketch the curve. State the domain and range.}

Example: Parametric equation of an ellipse

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Example: Parametric equation of a hyperbola

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