Re: Ellipses word problem

Hi, Greymalkin.

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 $\displaystyle x$ and $\displaystyle y$ must satisfy the equation

$\displaystyle \frac{x^{2}}{(25)^{2}}+\frac{y^{2}}{(14)^{2}}=1,$

where 25 is the major radius of the ellipse, and 14 is the minor radius. What you determined in your work was that the $\displaystyle x$ coordinate of the point we're interested is $\displaystyle x=-19$. Our goal is to know what the height $\displaystyle y$ is at this point; to determine this we can use the ellipse equation above since we know what$\displaystyle x$ is at the point of interest.

Does this help? Let me know if anything is unclear.

Good luck!

Edit: I was thinking of the bank on the left of the picture, that's why I have $\displaystyle x=-19$ above, but if you wanted to consider the right bank you could use $\displaystyle x=19$. It's all academic because we're going to square things in the equation of the ellipse anyways!