Chapter 10 - Section 10.5 - Conic Sections - 10.5 Exercises - Page 680: 16

Foci: $( -1\pm \sqrt 2,2 )$ Vertices : $( -1 \pm \sqrt 3,2)$

$x^2+3y^2+2x-12y+10=0$ Rewrite as $\frac{(x+1)^2}{(\sqrt 3)^2}+\frac{(y-2)^2}{1}=1$ $c^2=a^2-b^2=3-1=2$ $c=\sqrt 2$ Foci: $( -1\pm \sqrt 2,2 )$ Vertices : $( -1 \pm \sqrt 3,2)$