If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

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 x-axis.

This can be diagrammatically represented as

The equation of the parabola is of the form y² = 4ax (as it is opening to the right).

Since the parabola passes through point A(5, 10)

Then,

⇒ 10² = 4a (5)

⇒ 100 = 20a

⇒ a = 100/20 = 5

Therefore,

the focus of the parabola is (a, 0) ⇒ (5, 0),

which is the mid-point of the diameter.

Hence, the focus of the reflector is at the mid-point of the diameter

NCERT Solutions Class 11 Maths Chapter 11 Exercise ME Question 1

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus

Summary:

The focus of the parabola is (5, 0), which is the reflector is at the mid-point of the diameter