Challenging Question - help a brother

Hello,

thanks in advance for anyone who can help me.

this question relates to linear quadratic systems

the question is:

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

I thought maybe to help, I would put the question before this one, which relates to this question.

It goes like this

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.

I figured out how to do this by subbing, x+k into the other equation, and then using discriminants to find out the values of k that would work.

im confused on the generalization question though.

Again, thanks to anyone who can help me