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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 form the vertex of the parabola?

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Solution

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.
The equation of the parabola is of the form x2=4ay (as it is opening upwards)
Since, the parabola passes through point (52,10)
(52)2=4a(10)
a=254×4×10=532
So, the equation of arch of parabola is
x2=58y

When y=2m
x2=54
x=54m
AB=2×54m=2×1.118m(approx)=2.23m(approx)
So, the arch is 2 m from the vertex of the parabola, its width is approximately 2.23 m

404000_419539_ans_30760dc8e40c4ecd9184da647df3c612.png

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