9y^2-8x^2+72y+16x+64=0
give the exact coordinates of any four points on the hyperbola

- toxicsugar22

9y^2-8x^2+72y+16x+64=0
give the exact coordinates of any four points on the hyperbola

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- myininaya

let x=0 solve for y
let y=0 solve for x
you should get two solutions for each time
so that is 4 solutions

- toxicsugar22

can u help me put x for 0

- myininaya

x=0
so we have
9y^2+72y+64=0
do you know how to solve this?

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## More answers

- toxicsugar22

YES

- toxicsugar22

ITS A quadractic equation

- myininaya

thats right you sound happy lol i think

- toxicsugar22

yes

- toxicsugar22

cant we foil

- toxicsugar22

to make it smaller numbers

- myininaya

i dont think there are any common factors but you see if the polynomial is factorable if you like

- anonymous

hey myininaya can you help me out after with my trapezoidal rule question:)

- toxicsugar22

so how do i do this

- toxicsugar22

u do it and we will compare our answer

- toxicsugar22

ok i got mine

- toxicsugar22

answer

- toxicsugar22

did u get an anser

- anonymous

this is weird i never recall ever learning hyperbola's in high school or college.

- toxicsugar22

myininama are you still there

- myininaya

sorry i was away

- myininaya

\[y=\frac{-72\pm \sqrt{72^2-4*9*64}}{2*9}\]

- toxicsugar22

ok

- toxicsugar22

i got that

- toxicsugar22

and then help me furthur

- myininaya

with simplifying?

- toxicsugar22

yes

- toxicsugar22

please

- myininaya

the bottom is 18 because 2*9=18
i would be 72^2-4*9*64 in my calculator if i were you

- toxicsugar22

ok

- anonymous

exact answer i get is \[y=(-72\pm \sqrt{4968})\div18\]

- myininaya

y=(-72+ sqrt{329472})/18
y=(-72- sqrt{329472})/18

- toxicsugar22

that is te answer

- myininaya

lol hes right i accidently put + between the b^2 and the 4ac

- myininaya

hey beehive if you want your fractions to look cooler you can use
frac{5}{7} and this will give you 5/7 in the equation editor if you want

- anonymous

ok thanks.

- toxicsugar22

so myininaya how do u go from there

- myininaya

what do you mean?

- myininaya

you can find the other two points now if you want

- anonymous

\[y={-4} \pm \frac{\sqrt{4968}}{18}\]

- myininaya

we already let x be 0
now lets let y be 0 and we will stil get a quadratic like
-8x^2+16x+64=0

- myininaya

divide both sides by -8
so we have
x^2-2x-8=0
(x-4)(x+2)=0
x=4 and x=-2
so our four coordinates are (4,0), (-2,0), (0,-4+sqrt(4968)/18),(0,-4-sqrt(4968)/18)

- toxicsugar22

i dont think the last two points are correct

- toxicsugar22

can we simply it

- myininaya

what did you get when u did 72^2-4(9)(36)
i dont have my calculator
if it is 4968 then those are corret above

- myininaya

i only have this calcutor on computer and i dont like to use it

- toxicsugar22

i got 3888

- toxicsugar22

inm i got 2880

- myininaya

72^2=5184
4*9*64=2304
i mean 64 not 36

- anonymous

myininaya where did you get 36.
that's what i mean.

- myininaya

2880

- anonymous

2880 here also

- myininaya

lol that should be under the square root sign not 4 thousand something number

- toxicsugar22

ok thanks i got it

- anonymous

squareroot of 4968 i think

- myininaya

but 72^2-4(9)(36)=2880

- myininaya

i mean 64 not 36

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