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