## ERoseM 3 years ago The equation of a hyperbola is given by: 25x^2-16y^2+100x+96y=144 Rewrite the equation in standard form

1. dpaInc

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

2. dpaInc

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

3. ERoseM

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

4. dpaInc

yes... you're correct

5. dpaInc

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

6. ERoseM

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

7. dpaInc

|dw:1337817875892:dw|

8. ERoseM

|dw:1337817783416:dw|

9. dpaInc

|dw:1337817942410:dw|

10. dpaInc

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

11. ERoseM

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

12. dpaInc

shouldn't the right side be 100?

13. dpaInc

|dw:1337818132008:dw|

14. ERoseM

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

15. dpaInc

ooh ok, so the right side is 400..

16. dpaInc

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

17. dpaInc

the equation you ended up with...

18. ERoseM

|dw:1337818278093:dw|

19. dpaInc

yes.. do you know where the center is?

20. ERoseM

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?

21. dpaInc

wait...

22. dpaInc

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

23. ERoseM

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

24. dpaInc

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

25. ERoseM

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

26. dpaInc

equation?

27. dpaInc

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

28. dpaInc

good work...

29. ERoseM

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

30. dpaInc

yes... a=4 b= c=

31. ERoseM

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