.
In her post, @MathLover1 INCORRECTLY interprets the problem,
considering only the case when the straight line touches the circle.
The correct interpretation is to consider a general case of an intersection
("having at least one intersection point").
So, I came to bring a CORRECT SOLUTION.
....eq.1
.....eq.2
--------------------------------
substitute in eq.1
if the line meets the curve, there is at least one solution and it is a case if discriminant >=
so, use discriminant
...in your case , , and
ANSWER. k >= .
Solved (correctly).