Question

The focus of a parabolic mirror is at a distance of 8 cm from its centre (vertex). If the mirror 25 cm deep, find the diameter of the mirror.

Answer 1

Let the vertex be at the origin. 

VF = a = 8 cm 

The equation of the parabola is 

Y² = 4ax = 4(8)x = 32x

Depth of the mirror = x₁ = 25 cm. 

So, radius is 0. 

⇒ y² = 32(25) = 800 

y = √800 = 10√8 = 10 x 2√2 = 20√2

= Radius of the mirror

∴ Diameter of the mirror = 2 × 20√2 = 40 cm of the mirror.