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 negative y –axis.
This can be diagrammatically represented as
The equation of the parabola is of the form x2 = -4ay (as it is opening downwards).It is given that at base arch is 10m high and 5m wide.
Therefore, y = -10 and x = 5/2 from the figure above.
It can be clearly seen that the parabola passes through point
Therefore, the arch is in the form of a parabola whose equation is
We need to find width, when height = 2m.
Therefore, to find x, when y = -2.
When, y = -2,
Hence, when the arch is 2m from the vertex of the parabola, its width is approximately 2.23m.
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