MHB Conics- Word problem with ellipses.

[Kyriakos1]

Hi. I am given the following problem. A small bridge is shaped like a semi-ellipse. Given that its maximum height is 3m and that its foci are located 4m from the centre find the height of the bridge at a distance of 2m from its edge.

So the problem give me the values b= 3 and c=4. With this we can find a. a^2= c^2 + b^2. 16 + 9 = 25 so a = 5. From there though I am stuck.. what does 2m from the edge represent? 2m away from from vertices (-5,0) and/or (5,0)? and how do I find the height if that is the case?

 

[Opalg]

Hi. I am given the following problem. A small bridge is shaped like a semi-ellipse. Given that its maximum height is 3m and that its foci are located 4m from the centre find the height of the bridge at a distance of 2m from its edge.

So the problem give me the values b= 3 and c=4. With this we can find a. a^2= c^2 + b^2. 16 + 9 = 25 so a = 5. From there though I am stuck.. what does 2m from the edge represent? 2m away from from vertices (-5,0) and/or (5,0)?

Hi Kyriakos, and welcome to MHB! Yes, 2m from the edge must mean 2m from a vertex. So the $x$-coordinate will be $\pm3$.

and how do I find the height if that is the case?

You know that $a=5$ and $b=3$, so you should be able to write down the equation of the ellipse. Then you want to find the $y$-coordinate (the height) when $x = \pm3$.