## anonymous one year ago 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.

1. anonymous

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

2. anonymous

Ok @saseal

3. anonymous

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4. 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

5. anonymous

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

6. anonymous

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

7. anonymous

you can guess which one it is by now :)

8. anonymous

C? @saseal

9. anonymous

yes

10. anonymous

Can you help me with a few others?

11. anonymous

ok

12. 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.

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

major axis is the longer side

17. anonymous

The y-axis

18. anonymous

correct

19. anonymous

now think where's the center

20. anonymous

theres no h and k here

21. anonymous

0,0

22. anonymous

there we have the both the center and vertices now

23. anonymous

What's the vertices though?

24. anonymous

center (0, 0) vertices (0, ±25)

25. anonymous

Oh ok!

26. anonymous

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27. anonymous

now we need to find c to get the foci

28. anonymous

$c=\sqrt{a^2-b^2}$

29. anonymous

Ok, so C = 15? @saseal

30. anonymous

+/- 15

31. anonymous

yes

32. anonymous

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

33. anonymous

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

34. anonymous

Could you help me with one more? @saseal

35. anonymous

yea

36. anonymous

sry im not looking at the pc all the time

37. anonymous

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

38. anonymous

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

39. anonymous

sry i fell asleep