#### Answer

The points are:
$(5,0); (-5,0); (0,-4); (0,4)$

#### Work Step by Step

We solve for y:
$2\sqrt{9+y^2} = 10 \\ \sqrt{9+y^2} = 5 \\ y = \pm4$
We solve for the x values of the y-intercepts as well:
$10 = \sqrt{(3+x)^2} + \sqrt{(3-x)^2} \\ 2x = \pm 10 \\ x = \pm 5$
To draw an ellipse, use curvy lines to connect the points found.