132. Form the canonical equation of a hyperbola with foci on the x-axis, given that the eccentricity $\varepsilon=1.5$, and the focal distance is 6.
Solution. Since $\left|F_{1}, F_{2}\right|=6$, then $2c=6$, i.e., $c=3$. Next, substituting the known values of $\varepsilon$ and $c$ into the formula $\varepsilon=c / a$, we get $1.5=3 / a$, from which $a=2$. Knowing $a$ and $c$, from the relation $c^{2}=a^{2}+b^{2}$ we find $9=4+b^{2}$, from which $b^{2}=5$.

Thus, the canonical equation of the hyperbola is $x^{2} / 4 - y^{2} / 5 = 1$.