The line L passing through the point P (1,2,) divides the circle x2 + y2-4x-5 = 0 into two arches. When the area of the smaller arch is the smallest, the equation of the line L is______ ．

The line L passing through the point P (1,2,) divides the circle x2 + y2-4x-5 = 0 into two arches. When the area of the smaller arch is the smallest, the equation of the line L is______ ．

The circle x2 + y2-4x-5 = 0 can be reduced to (X-2) 2 + y2 = 9, the coordinate of the center C of the circle is (2, 0), and the radius is 3. Let the line L and the circle x2 + y2-4x-5 = 0 intersect at points a and B, then when p is the midpoint of AB, the area of the smaller arch is the smallest, and the line between point P and circle C is perpendicular to the line L, ∵ KPC = 2 − 01 − 2 = - 2 ∵ K

Given two circles x ^ 2 + y ^ 2 = 9 and (x-4) ^ 2 + y ^ 2 = 4, we can find the linear equation of the common chord

X ^ 2 + y ^ 2 = 9 and (x-4) ^ 2 + y ^ 2 = 4
Subtract the two formulas to get - 8x + 16 = - 5
8x=21
x=8/21
The linear equation is x = 8 / 21

Given that the circle (X-2) ^ 2 + (y + 3) ^ 2 = 13 and the circle (x-3) ^ 2 + y ^ 2 = 9 intersect at two points a and B, then the linear equation and common chord length of chord AB are obtained

By subtracting two circles, the equation of the line where the intersecting string is located is obtained: (X-2) &# 178; + (y + 3) &# 178; - (x-3) &# 178; - Y & # 178; = 13-9x & # 178; - 4x + 4 + Y & # 178; + 6y + 9-x & # 178; + 6x-9-y & # 178; = 42x + 6y = 0, that is, x + 3Y = 0, circle 1, circle center (2, - 3), R

Given that circle C is symmetric about y axis, passing through point (1,0) and divided into two segments by X axis, the arc length ratio is 1:2, then the equation of circle C is ()
A. (x±33)2+y2＝43B. （x±33）2+y2=13C. x2+（y±33）2=43D. x2+（y±33）2=13

Let C (0, a) be the center of the circle, then the radius is ca. according to the ratio of the arc length of the circle divided into two segments by x-axis is 1:2, the center angle of the chord pair cut by x-axis is 2 π 3, so tan π 3 = | 1a |, a = ± 33, radius r = 43, so the equation of the circle is x2 + (Y ± 33) 2 = 43, so C