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Circle - Line Intersections

  1. Dec 6, 2006 #1
    1. The problem statement, all variables and given/known data
    I'm completely stuck on this question
    I'll write the whole thing down

    Consider the circle x² + y² = 25 and the line y = x + k. where k is any real number. Determine the values of k for which the line will intersect the circle in one, two or no points.

    PLEEEASE help me

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 6, 2006 #2
    Didn't you ask a question almost exactly like this the other day? What have you tried so far?
  4. Dec 7, 2006 #3


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    Staff Emeritus
    Science Advisor

    Points, (x,y), at which two curves intersect are x, y values that satisfy both equations. You are trying to find x and y that satisfy both x2+ y2= 25 and y= x+ k. If y= x+ k then the first equation becomes x2+ (x+ k)2= 25. That's a quadratic equation for x. When does a quadratic equation have two distinct solutions?
  5. Dec 7, 2006 #4
    nvm i got it yesterday lol
    thanx anyways
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