## Example: Parametric equation of a circle

## The following example is used.

A curve has parametric equations x = sin(t) – 2, y = cos(t) + 1 where t is any real number.

Show that the Cartesian equation of the curve is a circle and sketch the curve.

## Example: Parametric equation of a parabola

## The following example is used.

A curve has parametric equations x = cot(t) + 1 , y = cosec^{2}(t) – 4 where 0 < t < π

Show that the Cartesian equation of the curve 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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