Conic Sections

Question 1

How do you find the focus of a parabola with vertex (0,0)?

Answer 1

(0,p) for x2 = 4py
(p,0) for y2 = 4px

Question 2

How do you find the directrix of a parabola with vertex (0,0)?

Answer 2

y = -p for x2 = 4py
x= -p for y2 = 4px

Question 3

How do you find the focal length of a parabola with vertex (0,0)?

Answer 3

The value of p (for both functions)

Question 4

How do you find the focal width of a parabola with vertex (0,0)?

Answer 4

The absolute value of 4p (for both functions)

Question 5

How do you find the focus of a parabola with vertex (h,k)?

Answer 5

(h, k+p) for (x-h)2 = 4p(y-k)
(h+p,k) for (y-k)2 = 4p(x-h)

Question 6

How do you find the directrix of a parabola with vertex (h,k)?

Answer 6

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

Question 7

How do you find the focal length of a parabola with vertex (h,k)?

Answer 7

p for both functions

Question 8

How do you find the focal width of a parabola with vertex (h,k)?

Answer 8

The absolute value of 4p for both functions

Question 9

How do you find the foci of ellipses with center(0,0)?

Answer 9

1. (c,0) & (-c,0) for x2/a2 + y2/b2 = 1
2. (0,c) & (0,-c) for y2/a2 + x2/b2 = 1

Question 10

How do you find the vertices of ellipses with center(0,0)?

Answer 10

1. (a,0) & (-a,0) for x2/a2 + y2/b2 = 1
2. (0,a) & (0,-a) for y2/a2 + x2/b2 = 1

Question 11

What are the semimajor/semiminior and major/minor axis for all ellipses, regardless of the center points?

Answer 11

Semimajor/semiminor: a/b
major/minor: 2a/2b
*For both functions

Question 12

How do you find the foci of ellipses with center(h,k)?

Answer 12

1. (h+/- c, k) for (x-h)2/a2 + (y-k)2 / b2 = 1
2. (h, k +/- c) for (y-k)2/a2 + (x-k)2/b2 = 1

Question 13

How do you find the vertices of ellipses with center(0,0)?

Answer 13

1. (h+/- a, k) for (x-h)2/a2 + (y-k)2 / b2 = 1
2. (h, k +/- a) for (y-k)2/a2 + (x-k)2/b2 = 1

Question 14

How do you find the foci of hyperbolas with center (0,0)?

Answer 14

1. (+/- c,0) for x2/a2 - y2/b2 = 1
2. (0, +/- c) for y2/a2 - x2/b2 = 1

Question 15

1. What are the semitransverse/semiconjugate axis for hyperbolas?
2. What are the transverse/conjugate axis for hyperbolas?

Answer 15

1. a/b
2. 2a/2b

Question 16

How do you find the vertices of hyperbolas with center(0,0)?

Answer 16

1. (+/- a, 0) for x2/a2 - y2/b2 = 1
2. (0, +/- a) for y2/a2 - x2/b2 = 1

Question 17

How do you find the foci of hyperbolas with center(h,k)?

Answer 17

1. (h +/- c, 0) for (x-h)2/a2 - (y-k)2/b2 = 1
2. (0, k +/-c) for (y-k)2/a2 - (x-h)2/b2 = 1

Question 18

How do you find the verticies of hyperbolas with center(h,k)?

Answer 18

1. (h +/- a, 0) for (x-h)2/a2 - (y-k)2/b2 = 1
2. (0, k +/- a) for (y-k)2/a2 - (x-h)2/b2 = 1