Answer:
The coordinates of the point the bulb should be placed is (2, 0.25)
Step-by-step explanation:
The given equation of a parabola is presented as follows;
(x - 2)² = 5·(y + 1)
The point the bulb should be placed is the focus of the parabolic mirror to ensure a perfect (straight) beam
The general form of the equation of a parabola is (x - h)² = 4·p·(y - k)
The coordinates of the focus of the parabola for p > 0 f = (h, k + p)
By comparison, h = 2, k = -1, and p = 5/4
∴ The coordinates of the focus of the parabola, f = (2, -1 + 5/4) = (2, 0.25)
The coordinates of the point the bulb should be placed is at the focus, f = (2, 0.25).