(Solved): Please include steps! Now consider the parabola y=x2 with a mirrored interior. A ray of light tra ...

Please include steps!

Now consider the parabola $$y=x^2$$ with a mirrored interior. A ray of light travels vertically into the parabola and reflects off of the point where the tangent line has slope 1. - What is the point on the parabola where the slope is 1? - Use your work from 5 above to find the y-intercept of this reflected ray. Redo the last two bullet points if we are dealing with an arbitrary parabola $$y=x^2/(4a)$$. I claim that this y-intercept is the Focal point of the parabola and that any vertical ray of light Redo the last two bullet points if we are dealing with an arbitrary parabola $$y=x^2/(4a)$$. I claim that this y-intercept is the Focal point of the parabola and that any vertical ray of light will bounce off the parabola and pass through this point. We'll show this in step 7. 7. Focus Principle We've done most of the work so far, we just need to tie things together in a few short arguments.