How would this equation be simplified?

[Bluskyz]

Homework Statement

To satisfy my curiosity, I tried to come up with an equation that describes how a line reflects off a parabola. The equation I came up with is [(tan[2*arctan(-y/50)]*[1000-(y^2)])/100]+y
This equation works wonderfully but its just large and ugly.
The wolfram alpha site for this equation is:
http://www.wolframalpha.com/input/?i=[(tan[2*arctan(-y/50)]*[1000-(y^2)])/100]+y
It just helps visualize the equation. From there, I noticed that wolfram simplifies this down further to (-1500*y)/([y^2]-2500)
How would I go about simplifying the original equation to the nice one wolfram gives?

Homework Equations

[(tan[2*arctan(-y/50)]*[1000-(y^2)])/100]+y

The Attempt at a Solution

I have tried to look at many trig identities involving the tangent functions but none of them seem to help in this case. I have tried moving things around but everything I try just seems to stop with those ugly tangents still left.

 

[supermiedos]

You could use the identity:

tan(2x) = 2tanx/ (1- (tanx)^2 )

and tan(arctan x) = x

 

[Bluskyz]

I tried that but on the bottom, you would still be left with 1-(tanx)^2

 

[supermiedos]

but remember x = arctan(-y/50).
So, 1-(tanx)^2 = 1 - (tan[arctan(-y/50)]^2 = 1 - y^2/2500

 

[Bluskyz]

Yes! I see it now, thanks for your help :)