# Solutions to Problem Set 30

Math 211-03

11-20-2017

[Parametric equations]

1. Find parametric equations for the curve for .

Set the independent variable equal to the parameter, so . Plug this into the x-y equation to obtain . The parametric equations are

2. Find parametric equations for the curve for .

Set the independent variable equal to the parameter, so . Plug this into the x-y equation to obtain . The parametric equations are

3. Find the x-y equation for the curve given by the parametric equations

Note that

Alternatively, you can solve the first equation for t to get . Plugging this into the y-equation and simplifying gives the same result.

4. Find parametric equations for the segment from the point to the point .

The equations are

5. Find parametric equations for the vertical line . (Note that this line is not the graph of a function .)

6. Find parametric equations for the circle

Choose your parametrization so that the circle is traced out once in the counterclockwise direction as t goes from 0 to .

7. Find parametric equations for the circle

Choose your parametrization so that the circle is traced out once in the counterclockwise direction as t goes from 0 to .

Divide the circle equation by 36 and write it as

This has the same form as . So I can get a parametrization by

The equations are

Note: If you switch the sine and cosine, the circle is traced out clockwise.

8. Find the x-y equation for the curve given by the parametric equations

Solve the parametric equations for and :

Then

I can simplify the x-y-equation to

9. Find the x-y equation for the curve given by the parametric equations

One does not love a place the less for having suffered in it. - Jane Austen

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