According to the known conditions, there are:
1.P( 1, 1) is on the straight line L 1: 4x-3y- 1 = 0, and the straight line is tangent to the garden, so there must be p as the tangent point.
2. The slope of the straight line l 1 and l2 is equal to = > L1/L2. When two parallel lines are tangent to a circle, there must be: the distance between the two straight lines is equal to the diameter 2r.
Distance from P( 1, 1) to line l2: 4x-3y+4=0:
2r = | 4-3+4 |/√( 16+9)= 1,r= 1/2,
From the center of the circle (a, b) to P( 1, 1), the distance of the straight line l2 is equal to =r,
(a- 1)^2+(b- 1)^2=( 1/2)^2- 1
| 4a-3 b+4 |/√( 16+9)= 1/2-2
The solution of 1 2 equation;
a=3/5,b= 13/ 10,
The equation of a circle is: (x-3/5) 2+(y-13/10) 2 =1/4.
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