Chapter 11.6, Problem 42E

a.

To determine

To draw: the conics with various value of $d$ .

Explanation of Solution

Given information:

The polar equation is $r=\frac{ed}{1+e\sin \theta }$ .

Graph: since, $e=1$

to draw the conic, use the plotting point method, first find the points for $d=1$ ,

$\theta$	$r$
$\frac{\pi }{2}$	$\frac{1}{2}$
$0$	$1$
$2\pi$	$1$

Like the above table, find the points for different values of $d$ ,then join the points,

Thus graphs can be obtained as:

  

Interpretation: from the above graph it can be observed that the when $d$ close to $0$ , the graph shifted downward.

b.

To determine

To draw: the conics with various value of $e$ .

Explanation of Solution

Given information:

The polar equation is $r=\frac{ed}{1+e\sin \theta }$ .

Graph: since, $d=1$

to draw the conic, use the plotting point method, first find the points for $e=1$ ,

$\theta$	$r$
$\frac{\pi }{2}$	$\frac{1}{2}$
$0$	$1$
$2\pi$	$1$

Like the above table, find the points for different values of $e$ ,then join the points,

Thus graphs can be obtained as:

  

Interpretation: from the above graph it can be observed that the when $e$ close to $0$ , the becomes more elongated as $e\to 1^{-1}$ .