my teacher said anyone in my class who gets this question would get a prize in front of the whole school.... okay.... i exaggerate.... but still, i want to understand this.

the question is:

consider the circle x^2 + y^2 = 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. Repeat for the circle x^2 + y^2 = 49 and the line y = x+k.

generalize your results for a circle of radius r and the line y = x+k

Note: the question asks for you to do two. Dont worry about it, just explain the steps and i will understand it.

Thanks in advance