The straight line tangent to the straight line 3x+4y-2=0 and vertical is y+ 1=(4/3)(x-2), that is, 4x-3y-1= 0.

The center (a, b) is on this straight line, and the distance to point P is d=r, that is:

①4a-3b- 1 1=0，②|3a-4b-2|/√(3？ +4? )=r

Substitute y=0 into the cyclic equation and get: (x-a)? +b？ =r？ ，x 1=a+√(r？ -B? )，x2=a-√(r？ -B? )

The chord length obtained by cutting the positive semi-axis of X axis is 8=|x 1-x2|=2√(r? -B? ), which is r? -B? = 16 ③

① ② ③ Simultaneous solution: r=5, a=5, b=3.

So the circle equation is (x-5)? +(y-3)？ =25

Go and see for yourself after work @ @ @