Understanding the Minimum Test Score Requirement for Competitive Examinations

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Can anybody help me understand the solution to the problem at http://www.tutorvista.com/q/to-qualify-in-a-competitive-examination-candidates-must-score-in-the/q53911_86449 ?
 
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They give a pretty reasonable explanation. What part of it don't you understand?
 

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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