What does those extra constants indicate?

Question

Equation:$$16x^2-9y^2+32x+36y-164=0$$

I know that it's a hyperbola by reducing it to this: $$\frac{(x+1)^2}{9}-\frac{(y-2)^2}{16}=1$$

My question is that this is different from what i have studied in school to be hyperbola's equation:

$$\frac{(x)^2}{a^2}-\frac{(y)^2}{b^2}=1$$

So why is it so?

Answer 1

Uhh, i don't know your basics about conics. But this simply indicates about the shift of center from origin $(0,0)$ to $(-1,2)$.

Theory: $$\frac{(x-a)^2}{A^2}-\frac{(x-b)^2}{B^2}=1$$ means that the hyperbola is now centered at $(a,b)$.

Hope It solve's your problem.

Answer 2

It's not any different, just that center is shifted to (-1,2).

Answer 3

If the function can be expressed $f(x-a,y-b)$, $f(x,y)$ move from $(0,0)$ to $(a,b)$.