SOLUTION: A lamp whose bulb is placed on the focus has a focal diameter of 12 cm. a. find the equation of the parabola. b. find the diameter of the opening 20 cm from the vertex.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A lamp whose bulb is placed on the focus has a focal diameter of 12 cm. a. find the equation of the parabola. b. find the diameter of the opening 20 cm from the vertex.      Log On


   

Question 1170110: A lamp whose bulb is placed on the focus has a focal diameter of 12 cm.
a. find the equation of the parabola.
b. find the diameter of the opening 20 cm from the vertex.
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!


%28x-h%29%5E2=4a%28y-k%29

where (h,k) = (0,0) = the vertex and 4a = focal diameter



matrix%281%2C3%2C%0D%0Ax%5E2%2C%0D%0A%22%22=%22%22%2C%0D%0A12y%29

The black line is the focal diameter.

We want the length of the red line.

The end points are where y=20

matrix%281%2C3%2C%0D%0Ax%5E2%2C%0D%0A%22%22=%22%22%2C%0D%0A12y%29

matrix%281%2C3%2C%0D%0Ax%5E2%2C%0D%0A%22%22=%22%22%2C%0D%0A12%2820%29%29

matrix%281%2C3%2C%0D%0Ax%5E2%2C%0D%0A%22%22=%22%22%2C%0D%0A240%29

matrix%281%2C3%2C%0D%0Ax%2C%0D%0A%22%22=%22%22%2C%0D%0A%22%22+%2B-+sqrt%28240%29%29

matrix%281%2C3%2C%0D%0Ax%2C%0D%0A%22%22=%22%22%2C%0D%0A%22%22+%2B-+sqrt%2816%2A15%29%29

matrix%281%2C3%2C%0D%0Ax%2C%0D%0A%22%22=%22%22%2C%0D%0A%22%22+%2B-+4sqrt%2815%29%29

So the red line is twice the absolute value of x.

Answer: 8sqrt%2815%29, about 30.98

Edwin