Finding equation for Hyperbola, given 3 points. 
"A hyperbola passes through $(0,-1)$, $(2, -1.5)$ and $(-1, 0)$. Find its equation..."

How would I go working this out? Would the $x$ and $y$ asymp be $-1$?  
I dont just want an answer, coz I need to know how to do it
Thanks.
 A: Judging from this article and this random example I tried, you would need at least $5$ distinct points to uniquely determine a hyperbola.
What I can tell you is that, because the slope between $(-1,0)$ and $(0,-1)$ is steeper than between $(0,-1)$ and $(2,-1.5)$, the hyperbola will probably take the form of $$\frac{(x-x_0)^2}{a^2} - \frac{(y-y_0)^2}{b^2} = 1$$ where $(x_0,y_0)$ is the intersection of the asymptotes whose slopes are $\displaystyle \pm \frac{b}{a}$.
The circle is the only conic uniquely determined by $3$ different points. Everything else needs at least $5$. See this and this and this as examples of why $4$ points is still not enough.
A: Suppose that the hyperbola is given in rectangular coordinates, that is to say under the form $$y=\frac{a+b x}{c+d x}$$  Because all coefficients appear in the general formula, fix any of them equal to $1$ without any lost of generality. Here, we shall arbitrarily fix $d=1$. So, we consider $$y=\frac{a+b x}{c+ x}$$ The curve goes through three data points you are given and we have the parameters $a,b,c$ to identify. This leads us with three equations for three unknowns; using you data points in the order you gave them, we so have $$ -1 =\frac{a}{c}$$  $$-\frac{3}{2}=\frac{a+2 b}{c+2}$$ $$0=\frac{a-b}{c-1}$$  From the first equation, we immediately have $a=-c$, from the third $b=a=-c$ and the second then gives $c=2$.  
So the equation is $$y=\frac{-2x-2}{2+x}=-\frac{2 (x+1)}{x+2}$$ what you have to double check in order to verify that the solution is valid.  
I am sure you can take from here.
