If a straight line passes through the point P (- 3, - 32), and the distance between the center of circle x2 + y2 = 25 and the straight line is 3, then the equation of the straight line is___ ．

If a straight line passes through the point P (- 3, - 32), and the distance between the center of circle x2 + y2 = 25 and the straight line is 3, then the equation of the straight line is___ ．

When the slope of the straight line does not exist, the equation of the straight line is x = - 3, and the distance from the center of circle x2 + y2 = 25 (0,0) to the straight line is 3, which satisfies the meaning of the problem; when the slope of the straight line exists, let the slope of the straight line be K, then the equation is y + 32 = K (x + 3), that is, 2kx-2y + 6k-3 = 0, the distance from the center of circle x2 + y2 = 25 to the straight line is | 6k-3 | 4 + 4k2 = 3, | k = - 34, and the equation of the straight line is 3x + 4Y + 15 = 0 So the answer is: x = - 3 or 3x + 4Y + 15 = 0

If a line with a slope of 1 is tangent to the circle (x-1) ^ 2 (y + 1) ^ 2 = 2, then the equation of the line is

Center (1, - 1), radius √ 2
Let y = x + B, X - y + B = 1
r = |1 + 1 + b|/√2 = √2
|b + 2| = 2
B = - 4 or B = 0