Hyperbolas
Foci $A(x_a,y_a)$ and $B(x_b,y_b)$:
- Center: $\frac{1}{2}( A+B)$.
-
$
\mathcal{E}_c
=
\{
P \in \mathcal{P}|~~
d(A,P)-d(B,P)
=
2c
\},
~ c \in \mathbb{R}
$
- Triangular Inequality:
\[
d(A,P) \leq d(A,B)+d(B,P)
\]
\[
d(B,P) \leq d(A,B)+d(B,P)
\]
Thus:
\[
-d(A,B) \leq c \leq d(A,B)
\]
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