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