Answer to Question #270951 in Analytic Geometry for Angel Nodado

Question

A semi-elliptical archway over a one-way road has a height of 9 ft and width of 36 ft. Your van has a width of 12 ft and height of 8 ft. Will your van be able to clear the opening of the archway?

Answer 1

Suppose that the eqaution of of our semi-ellipse is

$$\dfrac{x^2}{18^2}+\dfrac{y^2}{9^2}=1, y\geq 0$$

If $x=6$

$$\dfrac{6^2}{18^2}+\dfrac{y^2}{9^2}=1$$

$$y^2=81-9, y\geq0$$

$$y=6\sqrt{2}$$

Since $6\sqrt{2}>8,$ then van will be able to clear the opening of the archway.