# 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?

**Solution:**

The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that the axis of the reflector is along the positive y-axis.

This can be diagrammatically represented as

The equation of the parabola is of the form x^{2} = 4ay (as it is opening upwards).

It can be clearly seen that the parabola passes through the point (5/2, 10).

Hence,

⇒ (5/2)^{2} = 4a(10)

⇒ a = 25/(4 × 4 × 10) = 5/32

Therefore, the arch is in the form of a parabola whose equation is x^{2} = (5/8)y

When y = 2,

x^{2} = (5/8) × 2

x^{2} = √5/4

x = 5/4

Therefore,

AB = 2 × 1.118 m (approx.)

= 2.236 m (approx.)

NCERT Solutions Class 11 Maths Chapter 11 Exercise ME Question 2

## 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?

**Summary:**

When the arch is 2 m from the vertex of the parabola, its width is approximately 2.236 m

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