# Circle - Line Intersections

1. Dec 6, 2006

### pokemeharder

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
Thanks

2. Relevant equations

3. The attempt at a solution

2. Dec 6, 2006

### d_leet

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

3. Dec 7, 2006

### 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?

4. Dec 7, 2006

### pokemeharder

nvm i got it yesterday lol
thanx anyways