Question

Parabola help :)

Answer 1

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

Answer 2

@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.

Answer 3

you don't need to complete the square for y since it's already done

think of -9y^2 as -9(y-0)^2

Answer 4

how did you go from step 2 to step 3?

Answer 5

factored out 16

Answer 6

idk where that -288 comes from

Answer 7

haha oh shoot, that was meant to be -400

Answer 8

I don't know where it came from either 0.0

Answer 9

wherever -288 is it's -400

Answer 10

ok

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

hrm that seems wrong?

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

center is still (4, 0)

Answer 19

\[\large \frac{y^2}{16}-\frac{(x-4)^2}{9}=1\]

is same as

\[\large \frac{(y-0)^2}{16}-\frac{(x-4)^2}{9}=1\]

Answer 20

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)

Answer 21

rearranging the equation wont change anything

Answer 22

(plus or minus)

Answer 23

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

Answer 24

right?

Answer 25

Yes center is the midpoint of vertices

Answer 26

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

Answer 27

a=4, b=3, c=5

Answer 28

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

Answer 29

asy: a/b(x-h)+k
so for mine it's

\[\pm \frac{ 4 }{ 3 }(x-4)\]

Answer 30

(with a y = before that)

Answer 31

looks good

Answer 32

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

Answer 33

is this correct so far? :)

Answer 34

(and DNE on the directrix as well)

Answer 35

looks gud

Answer 36

thank you so so much! ;)