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