Question

16. What are the coordinates of the foci?




17. What are the coordinates of the vertices?




18. Find the equation of the ellipse.

Answer 1

You can find the vertices just by looking at the graph (2, -1) and (2,-9)
the major axis is vertical in this case (it's always the longer one)
The distance between the two vertices is 8, so a or the semimajor axis is 4
Halfway between the two vertices is the center, or (2,-5)
If you find that point on the graph, you'll see the to the left and right the graph is exactly 3 squares from the center, so b or the semiminor axis is 3

You now have everything you need, and the formula for an ellipse is \[ \frac{ (x-h)^2}{ b^2 }+\frac{ (y-k)^2 }{ a^2 }=0\] when it's vertical

so then you'd have \[\frac{ (x-2)^2 }{ 9 }+\frac{ (y+5)^2 }{ 16}=0\] as your equation