# NCERT Class 11 Mathematics Solutions: Chapter 11 –Conic Sections Miscellaneous Exercise 11 Part 1

1. If a parabolic reflector is in diameter and deep, find the focus.

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 x-axis.

This can be diagrammatically represented as

The equation of the parabola is of the form (as it is opening to the right).

Since the parabola passes through point

So, the focus of the parabola is , which is the mid-point of the diameter.

So, the focus of the reflector is at the mid-point of the diameter.

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

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.

This can be diagrammatically represented as.

The equation of the parabola is of the form (as it is opening upwards).

It can be clearly seen that the parabola passes through point

So, the arch is in the form of a parabola whose equation is

When

(approx)

(approx.)

Hence, when the arch is from the vertex of the parabola, its width is approximately .