Question

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Answer 1

The origin of the coordinate plane is taken at the vertex of the arch in such a way that its vertical axis is along the positive y-axis. This can be diagrammatically represented as

The equation of the parabola is of the form x2 = 4ay (as it is opening upwards).
It can be clearly seen that the parabola passes through point (5/2,10)

Therefore, the arch is in the form of a parabola whose equation is X² =5/8y

Hence, when the arch is 2 m from the vertex of the parabola, its width is approximately 2.23 m.