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SAT & subject tests > math 2: conic sections > Flashcards

math 2: conic sections Flashcards

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SAT® Prep flashcards
1
Q

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

A

nappes of a right cone

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2
Q

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

A

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

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3
Q

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

A

left (p 0)

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4
Q

(parabola→x-orientation) the standard equation is

A

(y - k)² = 4p(x - h)

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5
Q

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

A

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

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6
Q

(parabola→ x-orientation) the vertex is

A

(h, k)

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7
Q

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

A

|p|

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8
Q

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

A

up (p > 0); down (p

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9
Q

(parabola→ y-orientation) the standard equation is

A

(x - h)²= 4p(y - k)

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10
Q

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

A

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

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11
Q

(parabola→ y-orientation) the vertex is

A

(h, k)

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12
Q

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

A

|p|

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13
Q

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

A

foci; constant

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14
Q

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

A

(h, k); major and minor axes

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15
Q

(ellipse→x-orientation) standard equation is

A

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

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16
Q

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

A

x- axis

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17
Q

(ellipse→x-orientation) the center is

A

(h, k)

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18
Q

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

A

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

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19
Q

(ellipse→x-orientation) the major axis is

A

2a units long

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20
Q

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

A

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

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21
Q

(ellipse→x-orientation)the minor axis is

A

2b units

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22
Q

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

A

major

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23
Q

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

A

c = √a² - b²

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

24
Q

(ellipse→y-orientation) standard equation is

A

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

25
Q

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

A

y-axis

26
Q

(ellipse→y-orientation) the center is

A

(h, k)

27
Q

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

A

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

28
Q

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

A

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

29
Q

(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 ….

A

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

30
Q

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

A

x- orientation

31
Q

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

A

y-orientation

32
Q

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

A

foci; constant

33
Q

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

A

vertex; asymptotic

34
Q

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

A

(h, k); transverse; conjugate

35
Q

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

A

sides

36
Q

(hyperbola→x-orientation) the standard equation is

A

(x - h)²/a² - (y - k)²/ b² = 1

37
Q

(hyperbola→x-orientation) the center is

A

(h, k)

38
Q

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

A

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

39
Q

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

A

transverse axis; horizontal; 2a

40
Q

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

A

transverse; c= √a² + b²

41
Q

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

A

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

42
Q

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

A

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

43
Q

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

A

hyperbola

44
Q

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

A

y - k = ± b/a (x-h)

45
Q

(hyperbola→y-orientation) the hyperbola opens

A

up and down

46
Q

(hyperbola→y-orientation) the standard equation is

A

(y - k)²/a² - (x - h)²/ b² = 1

47
Q

(hyperbola→y-orientation) the center is

A

(h, k)

48
Q

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

A

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

49
Q

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

A

vertical; 2a

50
Q

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

A

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

51
Q

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

A

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

52
Q

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

A

y - k = ± a/b (x-h)

53
Q

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

A

x-orientation

54
Q

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

A

y-orientation

55
Q

eccentricity: measure of an ellipse/ hyperbola’s degree of ….

A

elongation

56
Q

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

A

c/a; 1; c

57
Q

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

A

c/a; 1; c > a

SAT & subject tests (30 decks)

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