Answer
(a) Vertices: $V(±a,0)=V(±\sqrt 2,0)$
Foci: $F(±c,0)=F(±\sqrt {3},0)$,
Asymptotes: $y=±\frac{b}{a}x=±\frac{1}{\sqrt 2}x=±\frac{\sqrt 2}{2}x$
(b)
Length of the transverse axis:
$2a=2\sqrt 2$
(c)
Work Step by Step
$\frac{x^2}{2}-\frac{y^2}{1}=1$
Hyperbola with horizontal transverse axis:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$a^2=2$
$a=\sqrt 2$
$b^2=1$
$b=1$
$c^2=a^2+b^2=2+1=3$
$c=\sqrt {3}$
(a) Vertices: $V(±a,0)=V(±\sqrt 2,0)$
Foci: $F(±c,0)=F(±\sqrt {3},0)$,
Asymptotes: $y=±\frac{b}{a}x=±\frac{1}{\sqrt 2}x=±\frac{\sqrt 2}{2}x$
(b)
Length of the transverse axis:
$2a=2\sqrt 2$
