# Equation of hyperbola

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 $b^2$

• Have you done any work on this yet? – 5xum May 20 '14 at 7:00
• 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 – user152175 May 20 '14 at 7:04
• Try to post what you did by editing your question. This will make it much easier for us to help you... – 5xum May 20 '14 at 7:05
• 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 $(0,0)$). – Gerry Myerson May 20 '14 at 7:36

$$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$$
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.
• @user152175 try taking $1/a^2=t$ and $1/b^2=u$ then solve. 2 equations. 2 variables. – evil999man May 20 '14 at 7:57