SOLUTION: As I left collage 60 years ago my mathematics is rusty. I want to build a solar cooker with the dimensions as follows: Diameter = 24 inches Focus point is 6 to 8 inches. Wha

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Question 1157225: As I left collage 60 years ago my mathematics is rusty. I want to build a solar cooker with the dimensions as follows:
Diameter = 24 inches
Focus point is 6 to 8 inches.
What I have tried. F(Y) = 4aX^2 where a the focus of 6 inches. However when I plot it all the lines are linear.
thanks Dave
email address brotherdave@rogers.com
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Try +y%5E2+=+4a%2Ax+
The focus will be on the x-axis a units from the origin.
here's the plot with +a+=+5+:
+graph%28+500%2C+500%2C+-12%2C+12%2C+-12%2C+12%2C+sqrt%28+20x+%29%2C+-sqrt%28+20x+%29%29+
------------------
A vertical line through the focus intersects the parabola at
( a, 4a/2 ) and ( a, -4a/2 ), and with +a+=+5+
( 5, 10 ) and ( 5, -10 )
You can use +a+ to adjust diameter of the ( rotated ) parabola
which is the cooker.
Note that solving for +y+,
+y+=+sqrt%28+4a%2Ax+%29+ and
+y+=+-sqrt%28+4a%2Ax+%29+
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hope this helps