Chapter 9

Question 1

point slope formula

Answer 1

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

Question 2

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

Answer 2

opens up or down

Question 3

a parabola opens up if

Answer 3

p>0

Question 4

a parabola opens down if

Answer 4

p<0

Question 5

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

Answer 5

opens right or left

Question 6

a parabola opens right if

Answer 6

p>0

Question 7

a parabola opens left if

Answer 7

p<0

Question 8

focus

Answer 8

P from vertex

inside parabola

Question 9

distance formula

Answer 9

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

Question 10

d1=d2

Answer 10

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

Question 11

how to tell if ellipse/circle

Answer 11

B^2 -4AC<0

Question 12

how to tell if parabola

Answer 12

B^2-4AC=0

Question 13

how to tell if hyperbola

Answer 13

B^2-4AC>0

Question 14

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

Answer 14

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

x comes first

Question 15

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

Answer 15

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

Question 16

hyperbola: foci are ___ units from center

Answer 16

c units from center

c^2 = a^2 + b^2

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

Question 17

slope of asymptotes in hyperbola

and how to find asymptotes

Answer 17

if vertical:
y=+/- (b/a) • (x-h)

if horizontal:
y=+/- (a/b) • (x-h)

Question 18

general form of conics

Answer 18

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

Question 19

circle, using general form

Answer 19

A=C

Question 20

parabola, using general form

Answer 20

AC=0

Question 21

ellipse, using general form

Answer 21

AC>0

Question 22

hyperbola,using general form

Answer 22

AC<0

Question 23

find angle in rotation

Answer 23

cot 2a= A-C/B

Question 24

what does x= in rotation of conics

Answer 24

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

Question 25

what does y= in a rotation of conics

Answer 25

y=(x1) sin a + (y1) cos a

Question 26

distance “a” in an ellipse

Answer 26

distance from center to vertice

under x when the major axis is horizontal, under y when the major axis is vertical

Question 27

distance “b” in an ellipse

Answer 27

distance from center to covertice (shorter length)

under y when the major axis is horizontal, under x when the major axis is vertical

Question 28

foci in an ellipse

Answer 28

lie on the major axis

c distance from center

c^2= a^2 - b^2

Question 29

ellipse - major axis horizontal

Answer 29

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

Question 30

ellipse - major axis is vertical

Answer 30

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

Question 31

eccentricity of an ellipse

Answer 31

the closer “e” is to zero, the more oval, or eccentric, the ellipse is

e=c/a

Question 32

distance a in hyperbola

Answer 32

distance from center to vertex

Question 33

area of an ellipse

Answer 33

area= pi • ab

Question 34

polar equations in parametric form:

x=?

Answer 34

x=f(t) *[cos(t)]

Question 35

polar equations in parametric form:

y=?

Answer 35

y=f(t)*[sin(t)]

Question 36

special polar graph: limacon

a/b <1

Answer 36

Limacons Inner Loop

Question 37

special polar graphs: limacon

a/b=1

Answer 37

limacon, cardioid

Question 38

special polar graph: limacon

1<a></a>

Answer 38

dimpled limacon

Question 39

special polar graphs: limacon

a/b>=2

Answer 39

convex limacon

Question 40

special polar graphs: rose curves
r=acos(nx) / r=asin(nx)
n is odd

Answer 40

n petals if odd

Question 41

special polar graphs: rose curves
r=acos(nx) / r=asin(nx)
n=even

Answer 41

2n petals if even

Question 42

special polar graphs: circles
if sin
if cos

Answer 42

if sin=shifted up or down

if cos=shifted right or left

Question 43

how to use e to tell if ellipse

Answer 43

if e<1, ellipse

Question 44

how to use e to tell if parabola

Answer 44

e=1

Question 45

how to use e to tell if hyperbola

Answer 45

e>1

Question 46

polar equations of conics

Answer 46

r= (ep)/(1+- ecos(x))

or

r=(ep)/(1+- esin(x))

Question 47

how to tell if there’s a horizontal directrix above the pole

Answer 47

r=ep/1+esin(x)

Question 48

how to tell if there’s a horizontal directrix below the pole

Answer 48

r=ep/1-esin(x)

Question 49

how to tell if there’s a vertical directrix to right of pole

Answer 49

r=ep/1+ecos(x)

Question 50

how to tell if there’s a vertical directrix to left of pole

Answer 50

r=ep/1-ecos(x)