Answer:
The wire should be placed at a height of 2.25 inches from the bottom
Explanation:
With the assumption that the shape of the solar hot-dog cooker is a parabola. we have the equation for the shape given as y = a·x² + b·x + c
Whereby the coordinates of the vertex is taken as (h, k) = (0, 0), we have;
c = 0
∴ y = a·x² + b·x
From the diagram, we have;
When x = 6, y = 4
When x = -6, y = 4
Which gives;
4 = a·(-6)² + b·(-6) = 36·a - 6·b
4 = 36·a - 6·b.........................................(1)
4 = a·(6)² + b·(6) = 36·a + 6·b
4 = 36·a + 6·b........................................(2)
Subtracting equation (1) from equation (2) gives;
4 - 4 = 36·a - 6·b - (36·a + 6·b) = -12·b
0 = -12·b
b = 0
Therefore;
4 = 36·a - 6×0
a = 4/36 = 1/9
The focus = F(h, k + p)
p = 1/(4·a) = 1/(4 × 1/9) = 1/(4/9) = 9/4 in = 2.25 inches
The coordinates of the focus, F = (h, k + p) = (0, 9/4) = (0, 2.25)
Therefore, the wire should pass through the focus and placed at 2.25 inches above the bottom.