A car’s headlight contains a parabolic reflector. A special bulb with two filaments is used to produce the high and low beams. The filament placed at the focus produces the high beam and the filament placed off-focus produces the low beam. The equation of the reflector is y=1/12 x^2. How far from the vertex should the filament for the high beam be placed? The x and y values are in centimeters. Be sure to include the correct unit in your answer.
what equation should I use
To determine how far from the vertex the filament for the high beam should be placed, we need to find the x-coordinate of the focus of the parabolic reflector. The equation of the reflector is given as y = (1/12)x^2.
The standard form of a parabolic equation is y = 4px, where p is the distance from the vertex to the focus. Comparing this with the given equation, we can see that 4p = 1/12.
To find the value of p, we can rearrange the equation as p = (1/12) / 4 = 1/48.
Therefore, the distance from the vertex to the focus (where the filament for the high beam should be placed) is 1/48 centimeters.