# Denoting an interval

#### Niles_M

Hi

I have a position P determined by the point, at which a vector v points to. Now I have a function, which is only defined for the points on and inside a circle with radius 2 within P. Can I write this interval as

$$\displaystyle x,y \in (x-v_x)^2-(y-v_y)^2=4$$

?

Sincerely,
Niles.

#### Defunkt

MHF Hall of Honor
That is a bit informal. You can write it like this:

$$\displaystyle A := \{ (x,y) \in \mathbb{R} ^2 : \ (x - v_x)^2 - (y - v_y)^2 = 4 \}$$

And then you can let $$\displaystyle (x, y) \in A$$ which, if I understand correctly is what you're looking for.