WorksheetsParametrics and Polar Equations
Total questions: 30
Worksheet time: 3hrs 45mins
Name
Class
Date
1.
Eliminate the parameter. Convert the parametric equation to rectangular. x= 2+4t and y=-1+6t
a)
y=(3/2)x - 4
b)
t=(x-2)/4
c)
y=x - 4
d)
y= (2/3)x + 4
2.
What is the center and radius of the curve:
x=1+3cost
y=-2+3sint
x=1+3cost
y=-2+3sint
a)
(-1,2) , r=3
b)
(-1,2) , r=9
c)
(1,-2) , r=3
d)
(1,-2) , r=9
3.
In the xy plane the graph x=5t+2 and y=3t for -3<t<3 is a line segment with the slope
a)
3/5
b)
5/3
c)
3
d)
5
4.
Which point represents (3, 3π/4)?
a)
F
b)
E
c)
B
d)
A
5.
Which point represents the polar coordinate
(-4, -2π/3)?
(-4, -2π/3)?
a)
B
b)
F
c)
D
d)
A
6.
Which equation represents the polar graph?
a)
r = sin (4θ)
b)
r = 6 sin(2θ)
c)
r = 6 cos (2θ)
d)
r = cos (4θ)
7.
Which equation represents the polar graph?
a)
r = 6 + 6 sin θ
b)
r = 12 sin θ
c)
r = 4 - 3 sin θ
d)
r = 4 + 5 sin θ
8.
Which equation represents the polar graph?
a)
r = sin θ
b)
r = sin 4θ
c)
r = 4 sin θ
d)
r = 4 cos θ
9.
The values of t control the values of x and y but are not used when plotting the points on the coordinate plane.
a)
True
b)
False
10.
The parametric equation x = 3cos(t), y = 3sin(t) is a ..
a)
a circle
b)
an ellipse
c)
a hyperbolas
d)
parabola
11.
Eliminate the parameter. Convert the parametric equation to rectangular. x= t - 1 and y=t2 - 2
a)
y=(x+1)2 - 2
b)
t=x - 1
c)
x=t - 1
d)
y=t - 2
12.
Convert from parametric to rectangular: x = t - 4 and y = 2t + 1
hint: Solve for t and then sub into "y" equation.
hint: Solve for t and then sub into "y" equation.
a)
y = 2t - 4
b)
y = 2x + 9
c)
y = 2x + 4
d)
y = 2t - 3
13.
Write the pair of parametric equations in rectangular form then determine the shape of the graph.
x = 3 cos ⊖ and y = 5 sin ⊖
x = 3 cos ⊖ and y = 5 sin ⊖
a)
ellipse
b)
circle
c)
hyperbola
d)
parabola
14.
Write x = 2t and y = t2 + 3 in rectangular form .
a)
y = 4x2 + 3
b)
y = ¼ x2 + 3
c)
y = 4t2 + 12
d)
y = (x - 2)2 + 3
15.
Describe the curve
a)
Rose with 4 petals
b)
Rose with 8 petals
c)
Rose with 3 petals
d)
Inner loop limacon
16.
Describe the curve
a)
Rose with 3 petals
b)
Rose with 6 petals
c)
Rose with 4 peta;s
17.
Describe the curve
a)
Rose curve
b)
Spiral of Archimedes
c)
Lemniscate
d)
limacon
18.
Determine the type of polar graph
a)
rose curve
b)
limacon
c)
lemniscate
d)
spiral of Archimedes
19.
A cannonball is fired at a 45.0° angle and an initial velocity of 625 m/s. Assume no air resistance. How long until the cannonball hits the ground?
a)
75.4 s
b)
45.2 s
c)
62.3 s
d)
90.2 s
20.
Kait hits the golfball at an angle of 27° with the horizontal at an initial speed of 22 m/s. How far has the ball traveled horizontally after 2 seconds?
a)
50.068 meters
b)
19.976 meters
c)
39.204 meters
d)
42.077 meters
21.
Convert the polar coordinates to rectangular form.
(6, 2π/3)
(6, 2π/3)
a)
( -3, 3)
b)
(3, 3√3)
c)
(-3, 3√3)
d)
(3, -3√3)
22.
Convert the polar coordinates (r, θ) to rectangular form (x, y).
a)
( -3, 3)
b)
(3, 3√3)
c)
(-3, 3√3)
d)
(3, -3√3)
23.
Covert the Cartesian rectangular equation to polar form.
a)
r² = 81
b)
r = 3
c)
r = 4.5
d)
r sin θ = 9
24.
Which equation represents the polar graph?
a)
r = sin 4θ
b)
r = 6 sin 2θ
c)
r = 6 cos 2θ
d)
r = cos 4θ
25.
Which equation represents the polar graph?
a)
r = 6 + 6 sin θ
b)
r = 12 sin θ
c)
r = 4 - 3 sin θ
d)
r = 4 + 5 sin θ
26.
Transform the polar equation to an equation in rectangular coordinates.
θ=π/3
θ=π/3
a)
y=√3 x, line through the pole, making an angle of π/3 with polar axis
b)
y=3x², quadratic line through pole with a point at π/3
c)
y=3x, line through the point of π/3
d)
y=√3x that does not go through pole
27.
Match the correct polar equation with the following graph:
a)
r=1+cosθ
b)
rsinθ=2
c)
r=1-2sinθ
d)
r=2
28.
Match the correct polar equation with the following graph:
a)
rcosθ=2
b)
rsinθ=2
c)
r=2cosθ
d)
r=2sinθ
29.
Match the correct polar equation with the following graph:
a)
r=2cosθ
b)
rcosθ=2
c)
r=2sinθ
d)
r=2
30.
Identify the polar equation:
r=1-3cosθ
r=1-3cosθ
a)
Limacon with inner loop
b)
Limacon without inner loop
c)
rose
d)
spiral
100 %
