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formulas

1
Q

What is the LRN1 and LRN2 if the parabola opening is right and the vertex is not in the origin?

A

LRN1(h+a,k+2a)
LRN2(h+a,k-2a)

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2
Q

What is the LRN1 and LRN2 if the equation is (y-k)²=4a(x-h) and the vertex is not in the origin?

A

LRN1(h+a,k+2a)
LRN2(h+a,k-2a)

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3
Q

What is the focus if the parabola opening is left and the vertex is not in the origin?

A

(h-a,k)

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4
Q

What is the opening of parabola if the focus is (h+a,k) and the vertex is not in the origin?

A

Right

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5
Q

What is the AS of parabola if it opens left and the vertex is in the origin?

A

y = 0

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6
Q

What is the AS of parabola if it opens right and the vertex is in the origin?

A

y = 0

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7
Q

What is the LRN1 and LRN2 if the parabola opening is downward and the vertex is not in the origin?

A

LRN1(h+2a,k-a)
LRN2(h-2a,k-a)

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8
Q

What is the focus if the directrix is y=k-a and the vertex is not in the origin?

A

(h,k+a)

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9
Q

What is the parabola opening if the equation is y²=4ax and the vertex is in the origin?

A

Right

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10
Q

What is the diretrix of parabola if it opens downward and the vertex is in the origin?

A

y = a

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11
Q

What is the directrix if the parabola opening is left and the vertex is not in the origin?

A

x=h+a

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12
Q

What is the directrix if the parabola opening is downward and the vertex is not in the origin?

A

y=k+a

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13
Q

midpoint formula

Circle

A

x = x² + x¹ / 2 or y = x² + x¹ / 2

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14
Q

What is the diretrix of parabola if it opens upward and the vertex is in the origin?

A

y = -a

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15
Q

What is the parabola opening if the equation is y²=-4ax and the vertex is in the origin?

A

Left

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16
Q

What is the equation of parabola if it opens downward and the vertex is in the origin?

A

x² = -4ay

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17
Q

What is the focus if the LRN1(h+2a,k+a)
LRN2(h-2a,k+a) and the vertex is not in the origin?

A

(h,k+a)

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18
Q

What is the focus if the LRN1(h+2a,k-a)
LRN2(h-2a,k-a) and the vertex is not in the origin?

A

(h,k-a)

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19
Q

What is the focus if the directrix is y=k+a and the vertex is not in the origin?

A

(h,k-a)

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20
Q

What is the opening of parabola if the focus is (h,k-a) and the vertex is not in the origin?

A

Downward

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21
Q

What is the diretrix of parabola if it opens left and the vertex is in the origin?

A

x = a

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22
Q

What is the equation if the focus is (h+a,k) and the vertex is not in the origin?

A

(y-k)²=4a(x-h)

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23
Q

What is the opening of parabola if the focus is (h-a,k) and the vertex is not in the origin?

A

Left

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24
Q

What is the opening of parabola if the focus is (h,k+a) and the vertex is not in the origin?

A

Upward

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25
Q

What is the parabola opening if x²=-4ay and the vertex is in the origin?

A

Downward

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26
Q

What is the LR1 and LR2 of parabola if it opens right and the vertex is in the origin?

A

LR1=(a,2a)
LR2=(a,-2a)

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27
Q

What is the equation of parabola if it opens in the left and the vertex is in the origin?

A

y² = -4ax

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28
Q

What is the equation if the directrix is x=h+a and the vertex is not in the origin?

A

(y-k)²=-4a(x-h)

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29
Q

What is the directrix if the parabola opening is upward and the vertex is not in the origin?

A

y=k-a

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30
Q

What is the parabola opening if the focus is at (a,0) and the vertex is in the origin?

A

right

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31
Q

What is the diretrix of parabola if it opens right and the vertex is in the origin?

32
Q

The formula if the center is in the origin

Circle

A

x² + y² = r²

33
Q

What is the LR1 and LR2 of parabola if it opens downward and the vertex is in the origin?

A

LR1=(2a,-a)
LR2=(-2a,-a)

34
Q

What is the focus if the LRN1(h+a,k+2a)
LRN2(h+a,k-2a) and the vertex is not in the origin?

35
Q

What is the focus if the parabola opening is right and the vertex is not in the origin?

36
Q

What is the equation of parabola if it opens upward and the vertex is in the origin?

37
Q

What is the AS of parabola if it opens upward and the vertex is in the origin?

38
Q

What is the focus if the LRN1(h-a,k+2a)
LRN2(h-a,k-2a) and the vertex is not in the origin?

39
Q

What is the equation if the directrix is y=k-a and the vertex is not in the origin?

A

(x-h)²=4a(y-k)

40
Q

What is the equation if the focus is (h-a,k) and the vertex is not in the origin?

A

(y-k)²=-4a(x-h)

41
Q

What is the parabola opening if the equation is x²=4ay and the vertex is in the origin?

42
Q

What is the LR1 and LR2 of parabola if it opens upward and the vertex is in the origin?

A

LR1=(2a,a)
LR2=(-2a,a)

43
Q

What is the LR1 and LR2 of parabola if it opens left and the vertex is in the origin?

A

LR1 =(-a,2a)
LR2 =(-a,-2a)

44
Q

General formula of a circle

A

x² + y²+ 2hx + 2ky + h² + k² = 0

45
Q

What is the LRN1 and LRN2 if the parabola opening is left and the vertex is not in the origin?

A

LRN1(h-a,k+2a)
LRN2(h-a,k-2a)

46
Q

What is the equation if the parabola opening is downward and the vertex is not in the origin?

A

(x-h)²=-4a(y-k)

47
Q

What is the parabola opening if the focus is at (-a,0) and the vertex is in the origin?

48
Q

What is the opening of parabola if the directrix is y=k+a and the vertex is not in the origin?

49
Q

What is the equation if the parabola opening is upward and the vertex is not in the origin?

A

(x-h)²=4a(y-k)

50
Q

i

What is the focus if the directrix is x=k+a and the vertex is not in the origin?

51
Q

What is the equation if the directrix is x=h-a and the vertex is not in the origin?

A

(y-k)²=4a(x-h)

52
Q

What is the equation if the directrix is y=k+a and the vertex is not in the origin?

A

(x-h)²=-4a(y-k)

53
Q

What is the equation of parabola if it opens in the right and the vertex is in the origin?

54
Q

What is the LRN1 and LRN2 if the equation is (x-h)²=-4a(y-k) and the vertex is not in the origin?

A

LRN1(h+2a,k-a)
LRN2(h-2a,k-a)

55
Q

What is the LRN1 and LRN2 if the equation is (y-k)²=-4a(x-h) and the vertex is not in the origin?

A

LRN1(h-a,k+2a)
LRN2(h-a,k-2a)

56
Q

What is the focus if the directrix is x=h-a and the vertex is not in the origin?

57
Q

What is the equation if the parabola opening is right and the vertex is not in the origin?

A

(y-k)²=4a(x-h)

58
Q

The formula if the center is not in the origin

Circle

A

(x-h)²+(y-k)²=r²

59
Q

Standard formula of a circle

A

(x-h)² + (y-k)² = r²

60
Q

What is the focus of parabola if it opens left and the vertex is in the origin?

61
Q

What is the LRN1 and LRN2 if the equation is (x-h)²=4a(y-k) and the vertex is not in the origin?

A

LRN1(h+2a,k+a)
LRN2(h-2a,k+a)

62
Q

What is the directrix if the parabola opening is right and the vertex is not in the origin?

63
Q

What is the parabola opening if the focus is at (0,a) and the vertex is in the origin?

64
Q

What is the opening of parabola if the directrix is x=h-a and the vertex is not in the origin?

65
Q

What is the focus if the parabola opening is upward and the vertex is not in the origin?

66
Q

What is the AS of parabola if it opens downward and the vertex is in the origin?

67
Q

What is the equation if the parabola opening is left and the vertex is not in the origin?

A

(y-k)²=-4a(x-h)

68
Q

What is the focus of parabola if it opens downward and the vertex is in the origin?

69
Q

What is the equation if the focus is (h,k-a) and the vertex is not in the origin?

A

(x-h)²=-4a(y-k)

70
Q

What is the LRN1 and LRN2 if the parabola opening is upward and the vertex is not in the origin?

A

LRN1(h+2a,k+a)
LRN2Ch-2a,k+a)

71
Q

What is the opening of parabola if the directrix is y=k-a and the vertex is not in the origin?

72
Q

What is the parabola opening if the focus at (0,-a) and the vertex is in the origin?

73
Q

What is the focus of parabola if it opens upward and the vertex is in the origin?

74
Q

What is the focus if the parabola opening is downward and the vertex is not in the origin?

75
Q

What is the opening of parabola if the directrix is x=h+a and the vertex is not in the origin?

76
Q

What is the focus of parabola if it opens left and the vertex is in the origin?

77
Q

What is the equation if the focus is (h,k+a) and the vertex is not in the origin?

A

(x-h)²=4a(y-k)

Sem1 (15 decks)

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