$\"\"$

\

The parametric equations:

\

(a) $\"\"$ and $\"\"$ .

\

(b) $\"\"$ and $\"\"$ .

\

(c) $\"\"$ and $\"\"$ .

\

Observe the all parametric equations, the equations is in the form of $\"\"$ .

\

(a) Graph the parametric equations $\"\"$ and $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

The graph of $\"\"$ and $\"\"$ is defined any number, except $\"\"$ . \ \

\

$\"\"$

\

(b) Graph the parametric equations $\"\"$ and $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

$\"\"$ can be any number except those where $\"\"$ .

\

$\"\"$ .

\

The general solution is $\"\"$ .

\

$\"\"$ varies from $\"\"$ to $\"\"$ , so the graph of $\"\"$ and $\"\"$ only for $\"\"$ .

\

The minimum value of $\"\"$ is $\"\"$ , $\"\"$ .

\

$\"\"$

\

(c) Graph the parametric equations $\"\"$ and $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

The graph of $\"\"$ and $\"\"$ is defined for $\"\"$ .

\

$\"\"$

\

Observe the graphs (a), (b) and (c): \ \

\

In graph (a) $\"\"$ for any except $\"\"$ .

\

In graph (b) $\"\"$ for $\"\"$ .

\

In graph (c) $\"\"$ for $\"\"$ .

\

$\"\"$

\

The curve $\"\"$ is generated in (a), (b) and (c). \ \

\

In graph (a) $\"\"$ for any except $\"\"$ .

\

In graph (b) $\"\"$ for $\"\"$ .

\

In graph (c) $\"\"$ for $\"\"$ .