A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 2 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.

I do not have any idea where to start this. If you can link me to a specific Khan Academy video that teaches what this requires that would be great. Any help is appreciated. (I do not want the answer though.)

Question

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 2 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.

I do not have any idea where to start this. If you can link me to a specific Khan Academy video that teaches what this requires that would be great. Any help is appreciated. (I do not want the answer though.)

anonymous · Answer

The equation of an upward opening parabola can be written:$$y=4ax ^{2}$$where the focus is at (0,a).

anonymous · Answer

Note that for the upward opening parabola, a has to be positive.  If a is negative, the parabola opens downward.

anonymous · Answer

$$y = \frac{1}{8}x^2$$

Is that a possible answer? (Sorry for the hour late reply I was working one other problems from my book and I just noticed you replied.

anonymous · Answer

No.  This parabola has its vertex at the origin of the coordinate system.  Since it's pointing up, it's focus lies on the positive part of the y-axis, at (0,2).  Given the formula I gave you, the equation for this parabolic mirror has to be:$$y=4*2*x ^{2}=8x ^{2}$$