## Babynini one year ago Parabola help :)

1. Babynini

2. Babynini

$16x^2-128x-9y^2+400=0$ $16(x^2-8x)-9y^2+400=0$ $16(x^2-8x+16-16)-9y^2=-288$ $16(x-4)^2-256-9y^2=-288$ $16(x-4)^2-9y^2=-32$

3. Babynini

@jim_thompson5910 I know we just did one like this, but i'm not quite sure where to go next with 9y^2 because it has no match.

4. jim_thompson5910

you don't need to complete the square for y since it's already done think of -9y^2 as -9(y-0)^2

5. jim_thompson5910

how did you go from step 2 to step 3?

6. Babynini

factored out 16

7. jim_thompson5910

idk where that -288 comes from

8. Babynini

haha oh shoot, that was meant to be -400

9. Babynini

I don't know where it came from either 0.0

10. Babynini

wherever -288 is it's -400

11. jim_thompson5910

ok

12. Babynini

Yeah. So the thing i'm at right now is $16(x-4)^2-9y^2=-144$

13. Babynini

er so the right side is negative. So i divide everything by negative yeah?

14. Babynini

$\frac{ (x-4)^2 }{ -9}+\frac{ y^2 }{ 16 }=1$

15. Babynini

hrm that seems wrong?

16. Babynini

@ganeshie8 can you check this? :) it doesn't match up with the graph.

17. ganeshie8

Looks good, just rewrite it as $\large \frac{y^2}{16}-\frac{(x-4)^2}{9}=1$

18. Babynini

but that makes the center (-1,4)?

19. ganeshie8

center is still (4, 0)

20. ganeshie8

$\large \frac{y^2}{16}-\frac{(x-4)^2}{9}=1$ is same as $\large \frac{(y-0)^2}{16}-\frac{(x-4)^2}{9}=1$

21. Babynini

http://www.wolframalpha.com/input/?i=16x%5E2+%E2%88%92+9y%5E2+%E2%88%92+128x+%2B+400+%3D+0 that's where im confused because the center should be (4,4)

22. ganeshie8

rearranging the equation wont change anything

23. Babynini

(plus or minus)

24. Babynini

oooh oh i see! that's the vertex, not center.

25. Babynini

right?

26. ganeshie8

Yes center is the midpoint of vertices

27. ganeshie8

|dw:1433392386227:dw|

28. Babynini

ahh, ok! I wasn't sure about that, so that's where I was confused. Thank you :)

29. Babynini

a=4, b=3, c=5

30. Babynini

now how do I find vertex, foci, asymptotes, dirtrex?

31. Babynini

asy: a/b(x-h)+k so for mine it's $\pm \frac{ 4 }{ 3 }(x-4)$

32. Babynini

(with a y = before that)

33. ganeshie8

looks good |dw:1433393241031:dw|

34. ganeshie8

scroll down to double check ur answers http://www.wolframalpha.com/input/?i=focus+16x%5E2+%E2%88%92+9y%5E2+%E2%88%92+128x+%2B+400+%3D+0

35. Babynini

is this correct so far? :)

36. Babynini

(and DNE on the directrix as well)

37. ganeshie8

looks gud

38. Babynini

39. Babynini

thank you so so much! ;)

40. Babynini

|dw:1433393976693:dw|

41. ganeshie8

Excellent!!!