SOLUTION: Find the equation of a hyperbola in the form y²/M - x²/N = 1, M, N> 0 if the center is at the origin, the length of the conjugate axis is 10, and the foci are sqrt(29) units from

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Question 1183543: Find the equation of a hyperbola in the form y²/M - x²/N = 1, M, N> 0 if the center is at the origin, the length of the conjugate axis is 10, and the foci are sqrt(29) units from the center.
Found 3 solutions by MathLover1, Edwin McCravy, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

, , if the center is at the
if given the standard form , then foci have the form (,±), and the transverse axis is the y-axis
=>
the foci are at: ( , ) and (, )
in your case


the length of the conjugate axis is =>=>






then


and your equation is:





Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
 I think she confused the conjugate axis and the transverse axis. It's
easy to do.

 is a hyperbola that opens right and left.

b is the length of the semi-conjugate axis, so b = half of 10, so b = 5. 




a is the semi-transverse axis, which is the distance from the center to the vertex,
the foci are sqrt(29) units from the center.
c = the distance from the center to either of the foci.

The Pythagorean relation for all hyperbolas is 









The equation is



 

Edwin
 

Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
 .





The solution by Edwin is correct.





The solution by @MathLover1 is not correct.







/////////////






Notice





    Edwin, please look into your first formula and the comment after it.


    I think this comment must be re-edited in this way


        "  is a hyperbola that opens up and down. "


    If you agree, I will erase this notice as soon as I see your correction implemented in your post.







 

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