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