Simple problem - cant spot my own mistake

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Solved, thanks Tedjin.
 
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You're mistake is in this part:

x2 + (3x-100)2 = 10000
10x2 - 600x - 9900 = 0

You haven't expanded correctly.
 
Quite the oversight.

Thanks, Tedjin. I shall aptly punish myself.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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