a line with y-intercept 5 and positive slope is drawn such that this line intersect x^2+y^2 = 9. What is the least slope of such a line?

my solution:

the line through A (0,5) has at least slope, when it is tangent to the circle at B.

Let B= <AOB. Since < ABO = 90, then OB = 3, OA = 5, AB = 4

hence tanB = 3/4.

therefore, the minimum slope of that line is 3/4....

anyone has another solution of this problem? or anyone can add a solution to this problem? I owe you for such a concern .thank you very much. good day