Question

The parabolic reflector of an automobile headlight is 12 cm. in diameter and 4 cm. in depth. 

Answer 1

Let the equation of parabola is y² = 4ax

Given diameter ,OC = 4cm = x- coordinate of A

Given AB = 12 cm

AC = (1/2) AB = 6 cm

So, A = (4,6)

So, A lie on parabola and will satisfy the equation , y² = 4ax

So, 36 = 16a

a = (9/4)

So, focus of parabola is ((9/4),0)