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Asked by Madhu Last Modified
Answer 
Vishaka Bhutia
Home Tutor
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
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The equation of the parabola is of the form x2 = −-4ay (as it is opening downwards).
It can be clearly seen that the parabola passes through point (52,−10)52,-10.
(52)2=−4a(−10)522=-4a-10
⇒4a=254×10=58⇒4a=254×10=58
Therefore, the arch is in the form of a parabola whose equation is x2=−58yx2=-58y.
When y = −-2, x2=−58(−2)x2=-58-2
⇒x2=54⇒x2=54
⇒x=5√2⇒x=52
​
∴AB = 2×5√2m =5–√ m = 2.23 m (approx.)∴AB = 2×52m =5 m = 2.23 m (approx.)
Hence, when the arch is 2 m from the vertex of the parabola, its width is approximately 2.23 m.
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