#### Answer

The center of the ellipse is (3, -2), the major axis is horizontal and parallel to the x-axis, and the distance from the center of the ellipse to its vertices is a = 5 units; this implies that the coordinates of the vertices are $\left( -2,-2 \right)$ and $\left( 8,-2 \right)$.

#### Work Step by Step

Then the center of ellipse is given to be $\left( 3,-2 \right)$, and the center will be $\left( h,k \right)$
Now, we are comparing both centers to obtain:
$h=3,\,\,k=-2$.
And the major axis is horizontal and the vertex is $a=5$.
Then the vertices given by
$\left( h-a,k \right),\left( h+a,k \right)$.
Hence, the vertices are
$\left( 3-5,-2 \right)=\left( -2,-2 \right)$ and $\left( 3+5,-2 \right)=\left( 8,-2 \right)$.