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

[pokemeharder]

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

Homework Equations

The Attempt at a Solution

 

[d_leet]

Didn't you ask a question almost exactly like this the other day? What have you tried so far?

 

[HallsofIvy]

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?

 

[pokemeharder]

nvm i got it yesterday lol
thanx anyways