Question

Will Medal, just really need help!!
Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ±1 divided by 3.x.

Answer 1

looks like you are stuck with analytic geometry :)
now lets start with how standard form looks like\[\frac{ y^2 }{ a^2 } - \frac{ x^2 }{ b^2 } = 1\]

Answer 2

Ok @saseal

Answer 3

My answer choices are:
A. y squared over 144 minus x squared over 16 = 1
B. y squared over 16 minus x squared over 36 = 1
C. y squared over 16 minus x squared over 144 = 1
D. y squared over 36 minus x squared over 4 = 1

I'm between B and C

Answer 4

now we have the gradient y=a/b which is 1/3

Answer 5

and we know a is 4 so b gotta be 12 since the gradient have to match up

Answer 6

you can guess which one it is by now :)

Answer 7

C? @saseal

Answer 8

yes

Answer 9

Can you help me with a few others?

Answer 10

ok

Answer 11

Thanks! @saseal
Find the center, vertices, and foci of the ellipse with equation x squared divided by 400 plus y squared divided by 625 = 1.

Answer 12

\[\frac{ x^2 }{ 400 } + \frac{ y^2 }{ 625 } = 1\] this should be easy by now

Answer 13

\[\frac{ x^2 }{ 20^2 } + \frac{ y^2 }{ 25^2 } = 1\]

Answer 14

where do you think is the major axis of this egg?

Answer 15

major axis is the longer side

Answer 16

The y-axis

Answer 17

correct

Answer 18

now think where's the center

Answer 19

theres no h and k here

Answer 20

0,0

Answer 21

there we have the both the center and vertices now

Answer 22

What's the vertices though?

Answer 23

center (0, 0) vertices (0, ±25)

Answer 24

Oh ok!

Answer 25

now we need to find c to get the foci

Answer 26

\[c=\sqrt{a^2-b^2}\]

Answer 27

Ok, so C = 15? @saseal

Answer 28

+/- 15

Answer 29

yes

Answer 30

Ok so would my answer be:
Center: (0, 0); Vertices: (-25, 0), (25, 0); Foci: (-15, 0), (15, 0)

Answer 31

Or no. It would be:
Center: (0, 0); Vertices: (0, -25), (0, 25); Foci: (0, -15), (0, 15

Answer 32

Could you help me with one more? @saseal

Answer 33

yea

Answer 34

sry im not looking at the pc all the time

Answer 35

No problem. And I'm in a new chapter so:
Find the derivative of f(x) = 6 divided by x at x = -2.

Answer 36

And also:
Find the derivative of f(x) = 4x + 7 at x = 5.

@saseal

Answer 37

sry i fell asleep