Through the point (1, - 1), make the tangent of the circle x ^ 2 + y ^ 2-2x-2y + 1 = 0, and find the tangent equation

Through the point (1, - 1), make the tangent of the circle x ^ 2 + y ^ 2-2x-2y + 1 = 0, and find the tangent equation

The formula of circle equation is (x-1) ^ 2 + (Y-1) ^ 2 = 1, so the center of circle (1,1), radius r = 1,
Let the tangent equation be y = K (x-1) - 1,
Then the distance from the center of the circle to the straight line is equal to the radius of the circle,
So | 1 + 1 | / √ (k ^ 2 + 1) = 1,
The solution is k = ± √ 3,
Therefore, the tangent equation is y = ± √ 3 * (x-1) - 1

Through point (5,6), make the tangent of circle x ^ 2-2x + y ^ 2-2y-2 = 0, and find the tangent equation
The numbers I worked out were weird,

Circle: (x-1) &# 178; + (Y-1) &# 178; = 4;
Radius of center (1,1) = 2;
Let the tangent be y-6 = K (X-5), that is, kx-y-5k + 6 = 0;
So the distance from the center of a circle to this line = | k-1-5k + 6 | / √ (K & # 178; + 1) = 2;
|5-4k|/√(k²+1)=2;
25+16k²-40k=4k²+4;
12k²-40k+21=0;
Δ=1600-4×12×21=592;
k=(40±4√37)/24=(10±√37)/6;
The tangent equation is (10 ± √ 37) x / 6-y-5 (10 ± √ 37) / 6 + 6 = 0;
The numbers are troublesome

The tangent equation from point P (1, - 2) to circle x2 + y2-6x-2y + 6 = 0 is______ ．

Circle x2 + y2-6x-2y + 6 = 0 is transformed into the standard equation, and (x-3) 2 + (Y-1) 2 = 4. The center of the circle is C (3,1), and the radius is r = 2. When the line passing through point P (1, - 2) is perpendicular to the X axis, the equation is x = 1, and the distance from the center of the circle to the line is equal to the radius. At this time, the line is tangent to the circle, which is in line with the meaning. When the line passing through point P (1, - 2) is not perpendicular to the X axis, let the equation be y + 2 = K (x-1) ）That is, kx-y-k-2 = 0, the distance from circle C to the straight line d = R, we get | 3K − 1 − K − 2 | 1 + K2 = 2, the solution is k = 512, the equation of the straight line is y + 2 = 512 (x-1), and the simplification is 5x-12y-29 = 0

The solution set of the absolute value inequality | x | ≤ a (a ≥ 0) can be obtained as follows: the geometric meaning of | x | ≤ a on the number axis is "the distance to the origin does not exceed a", so
The solution set of is - a ≤ x ≤ A. (1) | x | ≤ 3 (2) | 2x-1 | ≤ 5

（1）∵|x|≤3
∴-3≤X≤3;；
（2）∵|2x－1|≤5
∴-5≤2x－1≤5
∴-4≤2X≤6
∴-2≤X≤3