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)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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