Chapter 9 Flashcards

(50 cards)

1
Q

point slope formula

A

y-y(1)= m (x-x(1))

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2
Q

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

A

opens up or down

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3
Q

a parabola opens up if

A

p>0

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4
Q

a parabola opens down if

A

p<0

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5
Q

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

A

opens right or left

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6
Q

a parabola opens right if

A

p>0

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7
Q

a parabola opens left if

A

p<0

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8
Q

focus

A

P from vertex

inside parabola

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9
Q

distance formula

A

d=sq root of (y1-y2)^2 + (x1-x2)^2

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10
Q

d1=d2

A

distance from given point to focus=distance from focus to tangent line’s y/x intercept

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11
Q

how to tell if ellipse/circle

A

B^2 -4AC<0

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12
Q

how to tell if parabola

A

B^2-4AC=0

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13
Q

how to tell if hyperbola

A

B^2-4AC>0

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14
Q

how to tell if hyperbola transverse axis is horizontal (right and left)

A

[(x-h)^2/a^2] -[(y-k)^2/b^2]

x comes first

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15
Q

how to tell if hyperbola transverse axis is vertical (top and bottom)

A

[(y-k)^2/a^2]-[(x-h)^2/b^2]

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16
Q

hyperbola: foci are ___ units from center

A

c units from center

c^2 = a^2 + b^2

foci = (h+/- c, k)
(h, k+/-c)

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17
Q

slope of asymptotes in hyperbola

and how to find asymptotes

A

if vertical:
y=+/- (b/a) • (x-h)

if horizontal:
y=+/- (a/b) • (x-h)

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18
Q

general form of conics

A

Ax^2+Cy^2+Dx+Ey+F=0

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19
Q

circle, using general form

A

A=C

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20
Q

parabola, using general form

A

AC=0

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21
Q

ellipse, using general form

22
Q

hyperbola,using general form

23
Q

find angle in rotation

A

cot 2a= A-C/B

24
Q

what does x= in rotation of conics

A

x= (x1)cos a - (y1)sin a

25
what does y= in a rotation of conics
y=(x1) sin a + (y1) cos a
26
distance "a" in an ellipse
distance from center to vertice under x when the major axis is horizontal, under y when the major axis is vertical
27
distance "b" in an ellipse
distance from center to covertice (shorter length) under y when the major axis is horizontal, under x when the major axis is vertical
28
foci in an ellipse
lie on the major axis c distance from center c^2= a^2 - b^2
29
ellipse - major axis horizontal
[(x-h)^2/a^2] + [(y-k)^2/b^2]
30
ellipse - major axis is vertical
[(x-h)^2/b^2] + [(y-k)^2/a^2]
31
eccentricity of an ellipse
the closer "e" is to zero, the more oval, or eccentric, the ellipse is e=c/a
32
distance a in hyperbola
distance from center to vertex
33
area of an ellipse
area= pi • ab
34
polar equations in parametric form: x=?
x=f(t) *[cos(t)]
35
polar equations in parametric form: | y=?
y=f(t)*[sin(t)]
36
special polar graph: limacon | a/b <1
Limacons Inner Loop
37
special polar graphs: limacon | a/b=1
limacon, cardioid
38
special polar graph: limacon | 1
dimpled limacon
39
special polar graphs: limacon | a/b>=2
convex limacon
40
special polar graphs: rose curves r=acos(nx) / r=asin(nx) n is odd
n petals if odd
41
special polar graphs: rose curves r=acos(nx) / r=asin(nx) n=even
2n petals if even
42
special polar graphs: circles if sin if cos
if sin=shifted up or down if cos=shifted right or left
43
how to use e to tell if ellipse
if e<1, ellipse
44
how to use e to tell if parabola
e=1
45
how to use e to tell if hyperbola
e>1
46
polar equations of conics
r= (ep)/(1+\- ecos(x)) or r=(ep)/(1+\- esin(x))
47
how to tell if there's a horizontal directrix above the pole
r=ep/1+esin(x)
48
how to tell if there's a horizontal directrix below the pole
r=ep/1-esin(x)
49
how to tell if there's a vertical directrix to right of pole
r=ep/1+ecos(x)
50
how to tell if there's a vertical directrix to left of pole
r=ep/1-ecos(x)