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.

- anonymous

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- anonymous

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

- anonymous

Ok @saseal

- anonymous

|dw:1439304877703:dw|

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- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

you can guess which one it is by now :)

- anonymous

C? @saseal

- anonymous

yes

- anonymous

Can you help me with a few others?

- anonymous

ok

- anonymous

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.

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

major axis is the longer side

- anonymous

The y-axis

- anonymous

correct

- anonymous

now think where's the center

- anonymous

theres no h and k here

- anonymous

0,0

- anonymous

there we have the both the center and vertices now

- anonymous

What's the vertices though?

- anonymous

center (0, 0) vertices (0, ±25)

- anonymous

Oh ok!

- anonymous

|dw:1439306628656:dw|

- anonymous

now we need to find c to get the foci

- anonymous

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

- anonymous

Ok, so C = 15? @saseal

- anonymous

+/- 15

- anonymous

yes

- anonymous

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

- anonymous

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

- anonymous

Could you help me with one more? @saseal

- anonymous

yea

- anonymous

sry im not looking at the pc all the time

- anonymous

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

- anonymous

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

- anonymous

sry i fell asleep

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