I think your approach is good, nice work! I think a small hint will get things going in the right direction.
Since you're taking the origin to sit "in the middle" so-to-speak, we know that and must satisfy the equation
where 25 is the major radius of the ellipse, and 14 is the minor radius. What you determined in your work was that the coordinate of the point we're interested is . Our goal is to know what the height is at this point; to determine this we can use the ellipse equation above since we know what is at the point of interest.
Does this help? Let me know if anything is unclear.
Edit: I was thinking of the bank on the left of the picture, that's why I have above, but if you wanted to consider the right bank you could use . It's all academic because we're going to square things in the equation of the ellipse anyways!