Expert: Paul Klarreich - 12/18/2007

Question
a reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 70 inches, how deep is the mirror in the center


answers

1225
----- in
1536

256
---- in
35

1225
----  in
18432

1225
----  in
128


Answer
Questioner:   chyjuan
Category:  Advanced Math
Private:  No
 
Subject:  precal
Question:  a reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 70 inches, how deep is the mirror in the center


answers

1225
----- in
1536

256
---- in
35

1225
----  in
18432

1225
----  in
128
................................
Hi, Chyjuan,

The standare equation of a parabola is  x^2 = 4ay, where a is the distance from the vertex to the focus.  In this case, you have a = 32 feet, or 384 inches.

x^2 = 4(384)y = 1536y

Now you want the y-coordinate corresponding to x = 35.

35^2 = 1536y

    35^2
y = -----
   1536

   1225
y = -----
   1536