An arch is in the form of a parabola with its axis vertical. The a | Filo
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Class 11

Math

3D Geometry

Conic Sections

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

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 -axis.

The equation of the parabola is of the form (as it is opening upwards)
Since, the parabola passes through point 


So, the equation of arch of parabola is

When



So, the arch is m from the vertex of the parabola, its width is approximately  m
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