Answer
See graph
Work Step by Step
We are given the hyperbola:
$-y^2+x^2=3$
Bring the equation to the standard form:
$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$
$\dfrac{x^2}{3}-\dfrac{y^2}{3}=1$
The transverse axis is parallel to the $x$-axis.
Determine $h,k,a,b,c$:
$h=0$
$k=0$
$a^2=3\Rightarrow a=\sqrt 3$
$b^2=3\Rightarrow b=\sqrt 3$
$c^2=a^2+b^2$
$c^2=3+3$
$c^2=6$
$c=\sqrt 6$
Determine the coordinates of the vertices:
$(h-a,k)=(0-\sqrt 3,0)=(-\sqrt 3,0)$
$(h+a,k)=(0+\sqrt 3,0)=(\sqrt 3,0)$
Determine the coordinates of the co-vertices:
$(h,k-b)=(0,0-\sqrt 3)=(0,-\sqrt 3)$
$(h,k+b)=(0,0+\sqrt 3)=(0,\sqrt 3)$
Determine the coordinates of the foci:
$(h-c,k)=(0-\sqrt 6,0)=(-\sqrt 6,0)$
$(h+c,k)=(0+\sqrt 6,0)=(\sqrt 6,0)$
Graph the hyperbola:
