math 2: conic sections

Question 1

conic sections are formed by the intersection of a plane and the 2

Answer 1

nappes of a right cone

Question 2

a parabola is the set of points that are equidistant from a

Answer 2

given point (focus) and a given line (directrix)

Question 3

(parabola→x-orientation) it opens to the …. or …

Answer 3

left (p 0)

Question 4

(parabola→x-orientation) the standard equation is

Answer 4

(y - k)² = 4p(x - h)

Question 5

(parabola→ x-orientation) the focus is …. and the directrix is ….

Answer 5

(h + p, k); x = h - p

Question 6

(parabola→ x-orientation) the vertex is

Answer 6

(h, k)

Question 7

(parabola→ x-orientation) the common distance from the parabola to the focus and directrix is

Answer 7

|p|

Question 8

(parabola→ y-orientation) it opens .. or …

Answer 8

up (p > 0); down (p

Question 9

(parabola→ y-orientation) the standard equation is

Answer 9

(x - h)²= 4p(y - k)

Question 10

(parabola→ y-orientation) the focus is… and the directrix is…

Answer 10

(h, k + p); y = k - p

Question 11

(parabola→ y-orientation) the vertex is

Answer 11

(h, k)

Question 12

(parabola→ y-orientation) the common distance from the parabola to the focus and directrix is

Answer 12

|p|

Question 13

an ellipse is the set of points whose distances from 2 given points (…) sum to a …..

Answer 13

foci; constant

Question 14

the center of an ellipse … is the intersection of its .. and ….

Answer 14

(h, k); major and minor axes

Question 15

(ellipse→x-orientation) standard equation is

Answer 15

(x - h)²/a² + (y - k)²/ b² = 1, where a² > b²

Question 16

(ellipse→x-orientation) the major axis is parallel to the

Answer 16

x- axis

Question 17

(ellipse→x-orientation) the center is

Answer 17

(h, k)

Question 18

(ellipse→x-orientation) the vertices are … and …, the endpoints of the … axis

Answer 18

(h-a, k); (h + a, k); major

Question 19

(ellipse→x-orientation) the major axis is

Answer 19

2a units long

Question 20

(ellipse→x-orientation)the endpoints of the minor axis are … and ….

Answer 20

(h, k - b); (h, k + b)

Question 21

(ellipse→x-orientation)the minor axis is

Answer 21

2b units

Question 22

(ellipse→x-orientation) the foci are on the … axis

Answer 22

major

Question 23

(ellipse→x-orientation)each focus is at a distance of … from the center, so the foci are at … and …

Answer 23

c = √a² - b²

h - c, k); (h + c, k

Question 24

(ellipse→y-orientation) standard equation is

Answer 24

(x - h)²/b² + (y - k)²/a² = 1, where a² > b²

Question 25

(ellipse→y-orientation) the major axis is parallel to the

Answer 25

y-axis

Question 26

(ellipse→y-orientation) the center is

Answer 26

(h, k)

Question 27

(ellipse→y-orientation) the vertices are .. and ...., the endpoints of the .. axis

Answer 27

(h, k - a); (h, k + a); major

Question 28

(ellipse→y-orientation) the endpoints of the minor ais are .... and ...

Answer 28

(h - b, a); (h + b, a)

Question 29

(ellipse→y-orientation) the foci are on the ... axis. Each focus is at a distance of .... from the center, so the foci are at ...., and ....

Answer 29

major; c = √a² - b²; (h, k - c); (h, k + c)

Question 30

if the larger denominator in an equation of an ellipse is under the x-term, the ellipse has a(n)

Answer 30

x- orientation

Question 31

if the larger denominator in an equation of an ellipse is under the y-term, the ellipse has a(n)

Answer 31

y-orientation

Question 32

a hyperbola is the set of points whose distances from 2 fixed points (...) differ by a ....

Answer 32

foci; constant

Question 33

a hyyperbola has 2 halves, each of which has a ... and sides that are ... to a pair of intersecting lines

Answer 33

vertex; asymptotic

Question 34

center of a hyperbola is ..., the intersection of its ... and ... axes

Answer 34

(h, k); transverse; conjugate

Question 35

(hyperbola→x-orientation) the hyperbola opens to the

Answer 35

sides

Question 36

(hyperbola→x-orientation) the standard equation is

Answer 36

(x - h)²/a² - (y - k)²/ b² = 1

Question 37

(hyperbola→x-orientation) the center is

Answer 37

(h, k)

Question 38

(hyperbola→x-orientation) the vertices are ... and ....

Answer 38

(h - a, k); (h + a, k)

Question 39

(hyperbola→x-orientation) the segment joining the 2 vertices is called the ..... this axis is ... and has length...

Answer 39

transverse axis; horizontal; 2a

Question 40

(hyperbola→x-orientation) the foci are on the.... axis. the distance between the center and each focus is ...

Answer 40

transverse; c= √a² + b²

Question 41

(hyperbola→x-orientation) the foci are .. and ...

Answer 41

(h - c, k); (h + c, k)

Question 42

(hyperbola→x-orientation) the vertical segment through the center with endpoints .. and ..., which has length ..., is called the ... axis

Answer 42

(h, k - b); (h, k + b); 2b; conjugate

Question 43

(hyperbola→x-orientation) the endpoints of the conjugate axis are not on the

Answer 43

hyperbola

Question 44

(hyperbola→x-orientation) the equations of the asymptotes are

Answer 44

y - k = ± b/a (x-h)

Question 45

(hyperbola→y-orientation) the hyperbola opens

Answer 45

up and down

Question 46

(hyperbola→y-orientation) the standard equation is

Answer 46

(y - k)²/a² - (x - h)²/ b² = 1

Question 47

(hyperbola→y-orientation) the center is

Answer 47

(h, k)

Question 48

(hyperbola→y-orientation) the vertices are ... and ...

Answer 48

(h, k - a); (h, k + a)

Question 49

(hyperbola→y-orientation) the transverse axis is ... and has length ...

Answer 49

vertical; 2a

Question 50

(hyperbola→y-orientation) the foci are ... and ...

Answer 50

(h, k - c); (h, k + c)

Question 51

(hyperbola→y-orientation) the conjugate axis is ..., has endpoints ... and ..., and has length ..

Answer 51

horizontal; (h - b, k); (h + b, k); 2b

Question 52

(hyperbola→y-orientation) the equations of the asymptotes are

Answer 52

y - k = ± a/b (x-h)

Question 53

if the x-term of the equation is positive, the hyperbola has a(n)

Answer 53

x-orientation

Question 54

if the y term is positive, the hyperbola has a(n)

Answer 54

y-orientation

Question 55

eccentricity: measure of an ellipse/ hyperbola's degree of ....

Answer 55

elongation

Question 56

the ecentricity of an ellipse is ..., which is less than ... since ...

Answer 56

c/a; 1; c

Question 57

the eccentricity of a hyperbola is also ..., which is greater than ... since ... in a hyperbola

Answer 57

c/a; 1; c > a