Question

C (3,4) tangent to the line y=1/3x-1/3

Answer 1

I do not understand what you are asking.

Answer 2

I wanna know the radius of the circle

Answer 3

The distance from a point (h,k) to the line Ax^2+Bx+C=0 is

|Ah+Bk+C|/√(A^2+B^2)
We can avoid messy fractions if we rewrite the line as
x-3y-1=0
So, that means the radius of your circle is
|1*3-3*4-1|/√(1^2+3^2) = 10/√10 = √10

Now you know the center and the radius, so just put into standard circle form.

Answer 4

Thank you