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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 $b^2$

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  • $\begingroup$ 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
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$$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$$

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.

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  • $\begingroup$ 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

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