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?
* * * * *
* | * P
* * - - - - o(10,14)
* | |*
* | 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.