If there are only two points on the circle C: (x-3) ^ 2 + (y + 5) ^ 2 = R ^ 2 and the distance from the two points to the straight line L: 4x-3y = 17 is 1, what is the value range of R?

If there are only two points on the circle C: (x-3) ^ 2 + (y + 5) ^ 2 = R ^ 2 and the distance from the two points to the straight line L: 4x-3y = 17 is 1, what is the value range of R?

Circle C: (x-3) &# 178; + (y + 5) &# 178; = R & # 178;
The center of the circle is (3, - 5)
The distance from the center of the circle to the straight line L: 4x-3y = 17 is d = | 4 * 3-3 * (- 5) - 17 | / √ (4 & # 178; + 3 & # 178;) = 10 / 5 = 2
Because there are only two points on the circle C: (x-3) ² + (y + 5) ² = R & #178; and the distance from the line L: 4x-3y = 17 is 1
Then 1 < R < 3