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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!