Question

3.742?

Answer 1

@Vocaloid

Answer 2

yeah good

Answer 3

the center is (-3,2), so h = -3 and k = 2
while the radius is 1

use the picture to write the appropriate equation

Answer 4

simplify, and be careful with parentheses

Answer 5

A

Answer 6

wait nvm

Answer 7

its either c or d

Answer 8

(x-h)^2 = (x-(-3))^2 = (x+3)^2
(y-k)^2 = (y-2)^2

Answer 9

D

Answer 10

excellent

Answer 11

point?

Answer 12

yeah good (had to look this one up tbh)

Answer 13

this is what we call "completing the square" in math

first we gather up the x terms

x^2 - 4x

then we take the b -term, divide it by 2, square it, then add it to both sides of the equation

x^2 - 4x + 2 + {the y terms but they're not important right now} = 10 + 2

then we factor x^2 - 4x + 2 = (x-2)^2

making h = 3

Answer 14

h = 2 sorry sorry

Answer 15

B

Answer 16

close but not quite

the term on the right hand side needs to be r^2 not just r

Answer 17

SO D

Answer 18

good

Answer 19

-4.5

Answer 20

i'm not sure that's right

y^2 + by + c = (y+2)^2 (this is taken from the circle equation), c is just some constant that's not important to solving the problem

so

y^2 + by + c = y^2 + 4y + 4

meaning b = 4

Answer 21

ooh i see what you did there

Answer 22

a is just a normal circle w/radius 1
b is not a circle, it's a line
c is not a circle (at least not in the real plane, it exists in the imaginary plane only)
so d, since this is a point

Answer 23

3.742

Answer 24

good

Answer 25

crap lemme just teach myself this again real quick

Answer 26

OKay

Answer 27

first find the midpoint of the two vertices, that will give you the center

Answer 28

midpoint is (2,2)

Answer 29

good, and each foci is 3 units away from the center so c = 3

the two vertices are the endpoints of the major axis, so the major axis is 14 units long, making a = 14/2 = 7

c^2 = a^2 - b^2

3^2 = 7^2 - b^2 making b^2 = 40

putting this all together:

Answer 30

so D

Answer 31

A?

Answer 32

yup A good

Answer 33

D?

Answer 34

good, D

Answer 35

what did you get as your c-value?

Answer 36

I actually used mathway :o

Answer 37

c^2 = b^2 - a^2

c = ?

Answer 38

\[\sqrt{(b+a)(b-a)}\]

Answer 39

using the values from the problem

Answer 40

this is the equation for an ellipse, identify what your a^2 and b^2 would be based on the problem

Answer 41

okay and then do a^2-b^2

Answer 42

yes

Answer 43

-1392

Answer 44

so a^2 = 64
b^2 = 52

c^2 = a^2 - b^2

what does c equal?

Answer 45

37.31

Answer 46

c^2 = 64 - 52

c = ?

Answer 47

good, so c = 2sqrt(3)

eccentricity = c/a = ?

Answer 48

c

Answer 49

good

Answer 50

C?

Answer 51

good

Answer 52

A?

Answer 53

A) is actually just a normal ellipse

I believe it's actually C since a degenerate ellipse is a point

Answer 54

A?

Answer 55

y needs to be the major axis so the bigger number needs to be below y

so C

Answer 56

D?

Answer 57

good (I'm working w/ a lot of people rn so you can tag me if I forget about you ;_;)

Answer 58

B?

Answer 59

@Vocaloid

Answer 60

the focal radii is c not a, so 2c

Answer 61

@Vocaloid

Answer 62

@Vocaloid

Answer 63

if we do a quick sketch, we can see that the foci + vertices line up on the y-axis

the midpoint is (0,0) using the midpoint of the two vertices

meaning the vertices are 4 units apart from the midpoint

so the a term is 4 meaning the y^2 term has to have 4^2 = 16 below it

making B the only possibility

Answer 64

also this q is getting laggy can we open a new one