SOLUTION: A searchlight reflector is designed so that a cross section through it axis is a parabola with the light source at its focus. If the reflector is 80 cm in diameter and 40 cm deep,

Question 103470: A searchlight reflector is designed so that a cross section through it axis is a parabola with the light source at its focus. If the reflector is 80 cm in diameter and 40 cm deep, how far from the opening is the light source?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a general equation for the parabola is (x-h)^2=4p(y-k)
where the vertex is located at (h,k) and p is the distance from vertex to focus

designating the bottom of the reflector as the origin (0,0); and letting 1 unit=40 cm makes the ends of the diameter (1,1) and (-1,1)

(x-0)^2=4p(y-0)^2 ... x^2=4py^2 ... 4p=x^2/y^2 ... 4p=1/1 ... 4p=1 ... 4p=40cm ... p=10 cm

10 cm from the vertex is 30 cm from the opening
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