Misc 1
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
Let equation of parabola be
y2 = 4ax
Here we need to find a (focus)
Hence, Taking Point A
and finding its coordinates
Parabola is 5 cm deep
Hence OC = 5 cm
So, x-coordinate of point A = 5
It can be seen from figure
AB = 20 cm
Since parabola is symmetric along x-axis
AC = 1 2 AB = 10 cm
Hence coordinates of point A is (5 , 10)
Since point A(5 , 10) lies on the parabola,
it will satisfy the equation of the parabola
Putting x = 5 and y = 10 in (1)
y2 = 4ax
102 = 4 5
100 = 20a
100 20 = a
5 = a
a = 5
Thus, Focus is (a , 0)
= (5 , 0)

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.