Question

The parametric representation of

2 2

1

4 9

x y

 

is given bya. x y   2cos , 3cos  

b. x y   2cos , 3sin  

c. x y   3cos , 2sin  

d. x y   2cos , 2sin  ​

Answer 1

Answer:

The parametric representation of

2 2

1

4 9

x y

 

is given bya. x y   2cos , 3cos  

b. x y   2cos , 3sin  

c. x y   3cos , 2sin  

d. x y   2cos , 2sin  ​

Your answerWe can eliminate the parameter by first solving the equation x(t)=2t+3 for t:

x(t) = 2t+3 x−3 = 2t t =

x−3

2

.

Substituting this into y(t), we obtain

y(t) = 3t−4 y = 3(

x−3

2

)−4 y =

3x

2

−

9

2

−4 y =

3x

2

−

17

2

.

The slope of this line is given by

dy

dx

=

3

2

. Next we calculate x′(t) and y′(t). This gives x′(t)=2 and y′(t)=3. Notice that

dy

dx

=

dy/dt

dx/dt

=

3

2

. This is no coincidence, as outlined in the following theorem

Step-by-step explanation:

Answer 2

Answer:

❤️

Step-by-step explanation: