$\"\"$

(a)

The polar equation is $\"\"$ .

where $\"\"$ is measured in tens of thousands of miles.

Construct a table and calculate the values of $\"\"$ on $\"\"$ .

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

Graph:

1. Draw a polar coordinate plane.

2. Use the points and polar axis symmetry to sketch the curve.

$\"\"$

(b)

Observe the graph:

The minimum distance the satellite will be from the earth occurs at $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Hence at $\"\"$ , $\"\"$ tens of thousand miles.

$\"\"$

Therefore the minimum distance is $\"\"$ miles.

The maximum distance the satellite will be from earth occurs at $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Hence at $\"\"$ , $\"\"$ tens of thousand miles.

$\"\"$

Therefore the maximum distance is $\"\"$ miles.

$\"\"$

(c)

The second satellite rectangular coordinates are $\"\"$ .

Find polar coordinates $\"\"$ .

Find $\"\"$ :

$\"\"$ .

Substitute $\"\"$ in the above equation.

$\"\"$

Find $\"\"$ :

$\"\"$

Since $\"\"$ , the angle is $\"\"$ .

Substitute $\"\"$ in the above equation.

$\"\"$

The second satellite passes through the point with polar coordinates $\"\"$ .

Find the location of first satellite, Substitute $\"\"$ in $\"\"$ .

$\"\"$

Hence $\"\"$ for first satellite and $\"\"$ for second satellite.

So the two satellites are $\"\"$ tens of thousand miles apart.

Therefore, the two satellites are $\"\"$ miles apart, hence do not collide.

$\"\"$

(a)

Graph the polar equtaion $\"\"$ .

$\"\"$

(b) The maximum distance is $\"\"$ miles and the minimum distance is $\"\"$ miles.