$\"\"$

\

The parametric equations are $\"\"$ and $\"\"$ .

\

Find the points at which the tangent is horizontal.

\

For Horizontal tangent: $\"\"$ .

\

Consider $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Equate $\"\"$ to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Horizontal tangents are at $\"\"$ .

\

Find the point of horizontal tangency.

\

At $\"\"$ :

\

$\"\"$ .

\

$\"\"$ .

\

At $\"\"$ , the point is $\"\"$ .

\

Horizontal tangent line occur at $\"\"$ .

\

$\"\"$

\

For vertical tangent: $\"\"$ .

\

Consider $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Equate $\"\"$ to $\"\"$ .

\

$\"\"$ .

\

Hence there are no solutions.

\

No vertical tangents.

\

$\"\"$

\

Graph:

\

Graph the parametric equations $\"\"$ and $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

Horizontal tangent line occur at $\"\"$ .

\

No vertical tangents.