Page: An ellipse has major axis of 10 units and minor axis of 8 units . If the center of the ellipse is at (5, 6,3). Write parametric equation of an ellipse.
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Solution:

$a=\frac{10}{2}=5, b=\frac{8}{2}=4$

$x_{c}=5, y_{c}=6, z_{c}=3$

$x=5+5 \cos \theta$

$y=6+4 \sin \theta$

$z=3$

$\therefore x_{i+1}=5+\left[\left(\mathrm{x}_{\mathrm{i}}-5\right) \cos \delta \theta-\frac{5}{4}\left(y_{i}-6\right) \sin \delta \theta\right]$

$\therefore y_{i+1}=6+\left[\left(\mathrm{y}_{\mathrm{i}}-6\right) \cos \delta \theta+\frac{4}{5}\left(x_{i}-5\right) \sin \delta \theta\right]$

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