The equation of a hyperbola is given by: 25x^2-16y^2+100x+96y=144
Rewrite the equation in standard form

- anonymous

- katieb

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- anonymous

ok.. it's complete the square time..
|dw:1337817367153:dw|

- anonymous

do you what you need in that first parenthesis to make it into a perfect square trinomial?

- anonymous

Yes, I do. It would be 4 in the first parenthesis and 9 in the second, correct? I am confused on what to do after that because the number on the other side of the equal sign is actually 444

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- anonymous

yes... you're correct

- anonymous

whatever you do to one side, you do to the other....
|dw:1337817614794:dw|

- anonymous

Yes, and then I get 400 on the right side and I'm unsure how to apply that to the other side.

- anonymous

|dw:1337817875892:dw|

- anonymous

|dw:1337817783416:dw|

- anonymous

|dw:1337817942410:dw|

- anonymous

oh... you're way ahead of me... :)

- anonymous

Is that right though? Is there anyway I can check the process because sometimes I keep going and it turns out wrong?

- anonymous

shouldn't the right side be 100?

- anonymous

|dw:1337818132008:dw|

- anonymous

144 is actually 444. I typed it in wrong originally and then explained it after

- anonymous

ooh ok, so the right side is 400..

- anonymous

the process is correct... if there are no calculation errors, the equation is correct.

- anonymous

the equation you ended up with...

- anonymous

|dw:1337818278093:dw|

- anonymous

yes.. do you know where the center is?

- anonymous

It would be (-2, -3) right? And its horizontal? How can I tell..I'm confused on when its different? Is a just always bigger?

- anonymous

wait...

- anonymous

this should be negative.... right?
|dw:1337818435775:dw|

- anonymous

Yes. Darn it. I should have seen that.
Thank you

- anonymous

here's your verification : center is at (-2, 3)
http://www.wolframalpha.com/input/?i=center+25x%5E2-16y%5E2%2B100x%2B96y%3D144

- anonymous

Thank you! That's perfect! The equation is horizontal right?

- anonymous

equation?

- anonymous

oh... yes.. this is a horizontal or left/right branch hyperbola...

- anonymous

good work...

- anonymous

And so a would be 4? Because in standard form it is 16 which is a^2?

- anonymous

yes...
a=4
b=
c=

- anonymous

b=5 and c= the square root of 41?

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