138. Form the equation of an equilateral hyperbola with foci on the $O x$ axis, passing through the point $M(4; -2)$.
Solution. Since point $M$ belongs to the hyperbola, its coordinates satisfy the canonical equation of the hyperbola:

$$
x^{2}-y^{2}=a^{2} ; 4^{2}-(-2)^{2}=a^{2} ; a^{2}=12
$$

Therefore, the desired equation is $x^{2}-y^{2}=12$.