Q. 1

# The focus of a parabolic mirror is at a distance of 6 cm from its vertex. If the mirror is 20 cm deep, find its diameter.

Answer :

Given: The focus of a parabolic mirror is at a distance of 6 cm from its vertex. And the mirror is 20 cm deep.

Need to find: Diameter of the mirror.

Here O is the vertex and A is the Focus. So, OA = a = 6 cm.

OD is the deep of the mirror = 20 cm

BC is the diameter of the mirror.

Equation of the parabola is, y^{2} = 4ax

⇒ y^{2} = 24x

The mirror is 20 cm deep. That means the x-coordinate of the points B, C and D is 20

Both the points, B and C are on the parabola. Hence, the points satisfies the equation of the parabola.

Therefore, y^{2} = 24 x 20 = 480

⇒ y = 21.9

So, the coordinate of B is (20, 21.9) and the coordinate of C is (20, -21.9).

Therefore, the diameter of the mirror is = (21.9 + 21.9) cm

= 43.8 cm

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A parabolic reflector is 5 cm deep and its diameter is 20 cm. How far is its focus from the vertex?

RS Aggarwal - Mathematics