Problem 19

Given information

The value of and is given by,

   

 

The value of the range is,

   

 

Step-by-step explanation

Consider the given interval,

   

 

Consider the given expressions,

   

 

The variation in the variable and is shown in Table 1

 

Table 1

 

The required graph is shown in Figure 1

 

Figure 1

 

From the given equation evaluate as,

   

 

From the given equation evaluate as,

   

 

Then,

   

 

The above equation is for the eclipse that is centred at .

 

The above equation ranges from to .

 

Thus, the curve represents the parametric equations traced by the particle that moves three times clockwise around the eclipse and start at the point .