Chapter 9 Conics

Question 1

What are the equations for an ellipse?

Answer 1

1. (x-h)^2/a^2 + (y-k)^2/b^2 = 1
2. (x-h)^2/b^2 + (y-k)^2/a^2 = 1

*a is the bigger number

Question 2

What are the properties of an ellipse?

Answer 2

1. vertex
2. co-vertex
3. focus

Question 3

If the largest distance of an ellipse is under the x,

1. How do you find the vertex?
2. How do you find the co-vertex?
3. How do you find the focus?

Answer 3

1. (h-a,k), (h+a,k)
2. Co-vertex: (h,k+b), (h,k-b)
3. Using, c^2 = a^2 - b^2, Focus: (h-c,k), (h+c,k)

Question 4

If the largest distance of an ellipse is under the y,

1. How do you find the vertex?
2. How do you find the co-vertex?
3. How do you find the focus?

Answer 4

1. (h,k-a), (h,k+a)
2. (h+b,k), (h-b,k)
3. Using, c^2 = a^2 - b^2, Focus: (h,k-c), (h,k+c)

Question 5

What are the equations for a hyperbola?

Answer 5

1. (x-h)^2/a^2 - (y-k)^2/b^2 = 1
2. (y-k)^2/b^2 - (x-h)^2/a^2 = 1

Question 6

What are the properties of a hyperbola?

Answer 6

1. vertex
2. focus
3. equations of asymptotes

Question 7

If x is positive for a hyperbola,

1. How do you find the vertex?
2. How do you find the focus?
3. How do you find the equations of asymptotes?

Answer 7

1. (h-a,k), (h+a,k)
2. Using, c^2 = a^2 + b^2, Focus: (h-c,k), (h+c,k)
3. y-k = +b/a(x-h), y-k = -b/a(x-h)

Question 8

If y is positive for a hyperbola,

1. How do you find the vertex?
2. How do you find the focus?
3. How do you find the equations of asymptotes?

Answer 8

1. (h,k-a), (h,k+a)
2. Using, c^2 = a^2 + b^2, Focus: (h,k-c), (h,k+c)
3. y-k = +a/b(x-h), y-k = -a/b(x-h)

Question 9

What are the equations for a parabola?

Answer 9

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

Question 10

What are the properties of a parabola?

Answer 10

1. vertex
2. focus
3. directrix
4. axis of symmetry

Question 11

If the x is squared for a parabola,

1. How do you find the vertex?
2. How do you find the focus?
3. How do you find the directrix?
4. How do you find the axis of symmetry?

Answer 11

1. (h,k)
2. (h+p,k)
3. x=h-p
4. y=k

*Open up is p>0, opens down if p<0

Question 12

If the y is squared for a parabola,

1. How do you find the vertex?
2. How do you find the focus?
3. How do you find the directrix?
4. How do you find the axis of symmetry?

Answer 12

1. (h,k)
2. (h,k+p)
3. y=k-p
4. x=h

*Open up is p>0, opens down if p<0