Thread: What is this an equation of?

1. What is this an equation of?

What does y^2-x^2=16 represent?

I know it's a hyperbola, but I read that:

if B2 − 4AC > 0, the equation represents a hyperbola;
if we also have A + C = 0, the equation represents a rectangular hyperbola.

Here A+C=0, but is this actually rectangular??? I thought it would just be a normal hyperbola....aren't rectangulars of the form xy=k

2. Re: What is this an equation of?

What does y^2-x^2=16 represent?

I know it's a hyperbola, but I read that:

if B2 − 4AC > 0, the equation represents a hyperbola;
if we also have A + C = 0, the equation represents a rectangular hyperbola.

Here A+C=0, but is this actually rectangular??? I thought it would just be a normal hyperbola....aren't rectangulars of the form xy=k
If you write this in standard form, you will have \displaystyle \begin{align*} \left(\frac{y}{4}\right)^2 - \left(\frac{x}{4}\right)^2 = 1 \end{align*}, so the asymptotes are \displaystyle \begin{align*} y = \pm \frac{4}{4}x = \pm x \end{align*}.

Their gradients are \displaystyle \begin{align*} 1, -1 \end{align*}, which multiply to give \displaystyle \begin{align*} -1 \end{align*}. Therefore the gradients are perpendicular, so yes, it's a rectangular hyperbola

3. Re: What is this an equation of?

ok, thanks! I think I got it!