An arc is in form of a parabola with axis vertical .The arc is 10m high and 5m Wide at base. Find the focus
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Step-by-step explanation:
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 x
2
=4ay (as it is opening upwards)
Since, the parabola passes through point (
2
5
,10)
(
2
5
)
2
=4a(10)
⇒a=
4×4×10
25
=
32
5
So, the equation of arch of parabola is
x
2
=
8
5
y
When y=2m
⇒x
2
=
4
5
⇒x=
4
5
m
∴AB=2×
4
5
m=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
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