Sketch an ellipse centered at the origin with focal points at $(0, 5)$ and $(0, −5)$. Mark a point $P$ on your ellipse and label it with the coordinates $(x, y)$.  

1. Write an expression for the sum of the distances from point $P$ to each of focal points.

   Hint (a):

   The distance from point $P$ to $(0, 5)$ is: $\sqrt{(x-0)^2+(y-5)^2}$

2. If the “string” used to create the ellipse is $15$ units long, use this distance with your expression from part (a) to create an equation.

3. See how far you can get rewriting your equation from part (b) in graphing form.