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Calc 2 9.1

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

 

 

 

 

Eliminate the parameter t to find a Cartesian equation for:

x=t^2

y=6+4t

x=Ay^2+By+C

where
A=______
and B=_____
and C=______

 

A= 0.0625

B= -3/4

C= 2.25

The work

Point Cost: 3

2.

 

 

 

 

 

 

Consider the parametric curve:
x=11sinø

The curve is (part of ) a circle and the cartesian equation
has the form

x^2+y^2=R^2

with R=______
The initial point has coordinates: x= ___, y= ___.
The terminal point has coordinates: x= ___ , y=___.
The curve is traced________

 

R= See the work


Initial x= 0 y= 15


Terminal x= 0, y= -15       


Traced: clockwise

The work

Point Cost: 1

3.

 

 

 

 

 

 

Consider the parametric curve:
x=4cosø,     y=9sinø,      -π/2≤ø≤π/2

The curve is (part of ) a ellipse and the cartesian equation
has the form

(x^2/a^2)+(y^2/b^2)=1

with a=________ and b=________
The initial point has coordinates: x= ___, y= ___.
The terminal point has coordinates: x= ___ , y=___.
The curve is traced________

 

a= see the work

b= see the work

Initial x= 0, y= -9

Terminal x= 0, y= 9

Traced: Counterclockwise

The work

Point Cost: 2

4.

 

 

 

Eliminate the parameter to find the cartesian equation
of the curve:

x= 8secø, y= 8tanø, -π/2<ø<π/2

The equation of the curve is: x=______

 

see the work
The work

Point Cost: 3

5.

 

 

 

 

 

Consider the parametric curve:
x=2+15cost,     y=4+15sint,      π/2≤t≤3π/2
The cartesian equation of the curve has the form
(x-h)^2+(y-k)^2=R^2 with
h=_____
k=_______ and
R=_______
The initial point has coordinates: x= ______, y= _____.
The terminal point has coordinates: x= ______, y= ________.
The curve is traced________

 

h= see the work

k= see the work

R= see the work

Initial x= 2, y=19

Terminal x=2, y= -11

Traced: Counterclockwise

The work

Point Cost: 2

6.

 

 

 

 

Eliminate the parameter to find the cartesian equation
of the curve:

y= cos^2ø

The equation of the curve is: y=______
from x=_____ to x=______

 

y= see the work

from x= -4 to 4

The work

Point Cost: 3

7.

 

 

 

 

 

 

Suppose parametric equations for the line segment
between (9, -5) and (0,4) have the form:

x=a+bt
y=c+dt

If the parametric curve starts at (9,-5) when t = 0
and ends at (0,4) at t= 1, then find a, b, c, and d.
a=____
b=____
c=____
d=____

 

a= see the work
b= -9
c= see the work
d= 9
The work

Point Cost: 2

8.

 

 

 

 

 

 

 

 

 

 

Assume time t runs from zero to 2π and that the unit
circle has been labled as a clock.
Match each of the pairs of parametric equations with the best
description of the curve from the following list.
A. Starts at 12 o’clock and moves clockwise one time around.
B. Starts at 6 o’clock and moves clockwise one time around.
C. Starts at 3 o’clock and moves clockwise one time around.
D. Starts at 9 o’clock and moves counterclockwise one time
    around.
E. Starts at 3 o’clock and moves counterclockwise two times
    around.
F. Starts at 3 o’clock and moves counterclockwise to 9 o’clock.

1. x= cos(2t); y= sin(2t)
2. x= -cos(t); y= -sin(t)
3. x= sin(t); y= cos(t)
4. x= -sin(t); y= -cos(t)
5. x= cos(t); y= -sin(t)

 

1. E

2. D

3. A

4. B

5. C

The work

9.

 

 

 

The circle (x-4)^2 +(y-7)^2= 16 can be drawn
with parametric equations.
Assume the circle is traced clockwise as the
parameter increases. If x= 2+2cost
then y=________

 

see the work
The work

Point Cost: 3

10.

 

 

 

The ellipse
(x^2/2^2)+(y^2/3^2)= 1
can be drawn with parametric equations. Assume the
curve is traced clockwise as the parameter increases.
If x=4cos(t)
then y=________

 

see the work
The work

Point Cost: 3

11.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Assume t is defined for all time. Enter the letter
of the graph below which corresponds to the curve traced by
the parametric equations.

 

A B C

 

D E
                                                                                                                             

1. B

2. A

3. D

4. C

5. E

The work