What is the equation of hyperbola if all axes (transverse axis, conjugate axis, principal axis) are along the coordinate axis (x and y axis), and passing through the point $(-3,4)$ and $(5,6)$.

I tried substituting the points by the standard equation and find $a^2$ and $b^2$

Equation 1 $(x+3)^2/a^2 - (y-4)^2/b^2 =1$

Equation 2 $(x-5)^2/a^2 - (y-6)^2/b^2 =1$

I just couldn't get $a^2$ and $b^2$

  • $\begingroup$ Have you done any work on this yet? $\endgroup$ – 5xum May 20 '14 at 7:00
  • $\begingroup$ Umm, i tried substituting the points in the standard equation of a hyperbola then finding the value of a^2 and b^2 but it's too complicated for me :) by the way all the axes are on the coordinate axis $\endgroup$ – user152175 May 20 '14 at 7:04
  • $\begingroup$ Try to post what you did by editing your question. This will make it much easier for us to help you... $\endgroup$ – 5xum May 20 '14 at 7:05
  • $\begingroup$ The equations you have written are for hyperbolas centered at $(-3,4)$ and at $(5,6)$, whereas the hyperbola you want goes through those points (and is centered at $(0,0)$). $\endgroup$ – Gerry Myerson May 20 '14 at 7:36


Substitute your given points as $(x,y)$ to form two equations with two variables as $a^2,b^2$. Note that $a^2,b^2$ can be both positive or both negative depending upon its orientation.

  • $\begingroup$ I plot the points and i'm sure that it's horizontal, i just couldn't get a^2 an b^2. I do not know how hahaha $\endgroup$ – user152175 May 20 '14 at 7:17
  • $\begingroup$ Plot the points? That's not what Awesome said to do. Try doing what Awesome said to do. $\endgroup$ – Gerry Myerson May 20 '14 at 7:37
  • $\begingroup$ Sorry for being dumb, yeah i alreday substitue it with what Awesome give, but i really do not know how to get the value of a and b. Sorry, i just really suck at math $\endgroup$ – user152175 May 20 '14 at 7:55
  • $\begingroup$ @user152175 try taking $1/a^2=t$ and $1/b^2=u$ then solve. 2 equations. 2 variables. $\endgroup$ – evil999man May 20 '14 at 7:57
  • $\begingroup$ Please write out what you get, user152175, when you substitute the given points into the equation Awesome gave. Then we'll have a better idea how to help you. $\endgroup$ – Gerry Myerson May 20 '14 at 13:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.