Chapter 12 Test

Question 1

Steps to convert P(x,y) –> P(r,θ)

Answer 1

r^2 = x^2 + y^2
θ = tan^-1 (y/x)

Question 2

Circle formula in polar mode

Answer 2

r = asinθ
r = acosθ

Question 3

For the circle formula, if a > 0, then the graph is…

Answer 3

Above if the equation is sin and right if the equation is cos

Question 4

For the circle formula, if a is less than 0, then the graph is…

Answer 4

Below if the equation is sin and left if the equation is cos

Question 5

Limasons formula

Answer 5

r = a ± bsinθ
r = a ± bcosθ

Question 6

For Limasons formula, if a = b, then the graph is a…

Answer 6

Cardiod (looks like a heart)

Ex: r = 2 + 2cosθ

Question 7

For Limasons formula, if a is less than b, then the graph is a…

Answer 7

Limason with a loop (a cardiod with a loop within it)

Ex: r = 2 + 3cosθ

Question 8

For Limasons formula, if a > b and 1 > a/b > 2, then the graph is a…

Answer 8

Limason with a dent

Ex: r = 4 + 3cosθ

Question 9

For Limasons formula, if a > b and a/b ≥ 2, then graph is a…

Answer 9

Convex limason (an ellipse with one side is straight)
Ex: r = 8 + 3cosθ

Question 10

Rose curve formula

Answer 10

r = asin(nθ)
r = acos(nθ)

Question 11

For Rose curve formula, if n is odd, there are ___ visible petals

Answer 11

n

Question 12

For Rose curve formula, if n is even, there are ___ visible petals

Answer 12

2n

Question 13

For Rose curve formula, a = ?

Answer 13

length of a petal

Question 14

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

1) What conic is it?
2) What are the key components of it?
3) How do you find each?
4) How do you find c?

Answer 14

1) Ellipse
2) Foci and Vertices
3) Vertices: (h ± a,k)
Foci: (h ± c,k)
4) c^2 = a^2 - b^2

Question 15

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

1) What conic is it?
2) What are the key components of it?
3) How do you find each?
4) How do you find c?

Answer 15

1) Ellipse
2) Foci and Vertices
3) Vertices: (h,k ± a)
Foci: (h,k ± c)
4) c^2 = a^2 - b^2

Question 16

x^2/a^2 - y^2/b^2 = 1

1) What conic is it?
2) What are the key components of it?
3) How do you find each?
4) How do you find c?

Answer 16

1) Hyperbola
2) Asymptotes, Vertices, and Foci
3) Asymptotes: (y - k) = ±b/a(x - h)
Vertices: (h ± a,k)
Foci: (h ± c,k)
4) c^2 = a^2 + b^2

Question 17

y^2/a^2 - x^2/b^2 = 1

1) What conic is it?
2) What are the key components of it?
3) How do you find each?
4) How do you find c?

Answer 17

1) Hyperbola
2) Asymptotes, Vertices, and Foci
3) Asymptotes: (y - k) = ±a/b(x - h)
Vertices: (h,k ± a)
Foci: (h,k ± c)
4) c^2 = a^2 + b^2

Question 18

(x - h)^2 = 4p(y - k)

1) What conic is it?
2) What are the key components of it?
3) How do you find each?
4) If p is positive which way is the graph facing? If p is negative?

Answer 18

1) Parabola
2) Vertex, Focus, Directrix
3) Vertex: (h,k)
Focus: (h, k + p)
Directrix: y = k - p
* +p = facing up
* -p = facing down

Question 19

(y - k)^2 = 4p(x - h)

1) What conic is it?
2) What are the key components of it?
3) How do you find each?
4) If p is positive which way is the graph facing? If p is negative?

Answer 19

1) Parabola
2) Vertex, Focus, Directrix
3) Vertex: (h,k)
Focus: (h + p, k)
Directrix: x = h - p
* +p = facing right
* -p = facing left