Thread: Conic Section Application Problems

Problem -
"A semielliptic archway has a height of 20 feet and a width of 50 feet. Can a truck 14 feet high and 10 feet wide drive under the archway without going into the other lane."

I understand that it pertains to an ellipse, but could it essentially be an upside-down hyperbola? Either way, I'm not sure where to actually start. Hopefully somebody can help me, and thank you.

Hello, HawthorneKitty!

A semielliptic archway has a height of 20 feet and a width of 50 feet. Can a truck
14 feet high and 10 feet wide drive under the archway without going into the other lane?

Code:

                20|
              * * * * *
          *       |       *  P
        *         * - - - - o(10,14)
       *          |         |*
                  |14       |
      *           |    10   | *
      * - - - - - * - - - - * *
      :    25     :    25     :

We have an ellipse with:

Its equation is: .

Question: Is the upper corner of the truck inside the ellipse?


Substitute the point into the left side of the equation:

. .


Since the value is less than 1, point is inside the ellipse.

Yes, the truck can drive through without going into the other lane.