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An arch is in the form of a parabola with its axis vertical. T

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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 from the vertex of the parabola?

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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 from the vertex of the parabola?

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Text solutionVerified

Solution:

x^{2} = 4 a y

point A and B lies on parabola

x^{2} = 4 a y

put A

(\frac{5}{2}, 10)

in the equation

(\frac{5}{2})^{2} = 4 \times a \times 10

a = \frac{25}{4 \times 4 \times 10} = \frac{25}{160}

a = \frac{5}{32}

x^{2} = 4 \times \frac{5}{32} \times y

x^{2} = \frac{5}{8} y

put

(x, 2)

x^{2} = \frac{5}{8} \times 2

x^{2} = \frac{10}{8} = \frac{5}{4}

x = \frac{5}{2}

P P^{'} = 5

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Question Text	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 from the vertex of the parabola?
Answer Type	Text solution:1
Upvotes	150