The equation of the line parallel to the line 2x-y + 1 = 0 and tangent to the circle x2 + y2 = 5 is () A. 2x-y + 5 = 0b. X2-y-5 = 0C. 2x + y + 5 = 0 or 2x + Y-5 = 0d. 2x-y + 5 = 0 or 2x-y-5 = 0

The equation of the line parallel to the line 2x-y + 1 = 0 and tangent to the circle x2 + y2 = 5 is () A. 2x-y + 5 = 0b. X2-y-5 = 0C. 2x + y + 5 = 0 or 2x + Y-5 = 0d. 2x-y + 5 = 0 or 2x-y-5 = 0

Let the tangent of a circle be 2x-y + M = 0, then the distance from the center of the circle (0, 0) to 2x-y + M = 0 d = | m | 22 + (− 1) 2 = r = 5, that is | m | = 5, and the solution is m = 5 or M = - 5, so the tangent equation is 2x-y + 5 = 0 or 2x-y-5 = 0, so D is selected

Solving the equation of the line parallel to the line y = x + 2 and tangent to the circle (X-2) ^ 2 + (Y-3) ^ 2 = 8
One more question
Given that the chord length of the line L passing through the point m (- 3, - 3) cut by the circle x ^ 2 + y ^ 2 + 4y-21 = 0 is 4 and the root sign is 5, the linear l equation can be solved

Let the equation of l be y = x + B
A straight line is tangent to a circle, that is, the distance from the center of the circle (2,3) to the straight line is equal to the radius
|2-3 + B | / √ 2 = 2 √ 2, the solution is b = 5, - 3
That is, l: y = x + 5, y = x-3

Solving the equation of the line parallel to the line x + y = 4 and tangent to the circle x ^ 2 + y ^ 2 = 8
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Parallel to the line x + y = 4
x+y+a=0
The distance from the center of the circle (0,0) to x + y + a = 0 is equal to the radius √ 8
So | 0 + 0 + a | / √ (1 ^ 2 + 1 ^ 2) = √ 8
|a|=4
So x + y + 4 = 0 and X + y-4 = 0

Given the circle C: X & # 178; + Y & # 178; - 4x-5 = 0, then the equation of the line passing through the shortest chord of point P (1,2) is given

Find out the center of the circle: (X-2) &# 178; + Y & # 178; = 1, center of the circle (2,0), radius = 1;
The slope of the line passing through the center (2,0) and point (1,2) K1 = (2-0) / (1-2) = - 2;
Then the slope of the vertical line K2 = 1 / 2;
Then the line passing through point P with slope K2 is Y-2 = 1 / 2 (x-1)
That is x-2y + 3 = 0