SOLUTION: a large reflecting telescope has a parabolic mirror that s 4 m eters in diamter and 25 centimeter deep. it requires a cage for the observer with an eyepiece at the focus of the mir

Question 1126329: a large reflecting telescope has a parabolic mirror that s 4 m eters in diamter and 25 centimeter deep. it requires a cage for the observer with an eyepiece at the focus of the mirror how far up the tube of the telescope must the cage be built? this design is called a prime focus telescope.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a large reflecting telescope has a parabolic mirror that s 4 meters in diameter and 25 centimeter deep. it requires a cage for the observer with an eyepiece at the focus of the mirror how far up the tube of the telescope must the cage be built?
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Make the parabola symmetric about the y-axis with its vertex at (0,-25)
--> 3 points: (-200,0), (0,-25) and (200,0)
Find an equation for the parabola.
---
ax^2 + bx + c = y
---
(0,-25) --> c = -25
(-200,0) --> 40000a -200b -25 = 0
(+200,0) --> 40000a +200b -25 = 0
---------------------------------------- Subtract
--> b = 0
======================
a = 25/40000 = 1/1600
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y = x^2/1600 - 25 is the parabola
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There are several ways to find the focus.
Can you do the rest?

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