What are the Intersection Points of a Circle and a Line?

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The discussion revolves around determining the intersection points between the circle defined by the equation x² + y² = 25 and the line represented by y = x + k, where k is a real number. The key approach involves substituting the line's equation into the circle's equation to form a quadratic equation in terms of x. The number of intersection points—one, two, or none—depends on the discriminant of this quadratic equation. The conversation highlights the importance of understanding how the discriminant indicates the nature of the solutions. Ultimately, the original poster found a solution to their problem.
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Homework Statement


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
Thanks


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The Attempt at a Solution

 
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Didn't you ask a question almost exactly like this the other day? What have you tried so far?
 
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?
 
nvm i got it yesterday lol
thanx anyways
 

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