The linear equation of chord length 8 passing through point a (- 1,10) and cut by circle x2 + y2-4x-2y-20 = 0 is______ .

The linear equation of chord length 8 passing through point a (- 1,10) and cut by circle x2 + y2-4x-2y-20 = 0 is______ .

The circle x2 + y2-4x-2y-20 = 0 is transformed into the standard equation as (X-2) 2 + (Y-1) 2 = 25. When the slope of the line is k, the linear equation is Y-10 = K (x + 1), that is, kx-y + K + 10 = 0 ﹤ the distance from the center of the circle (2,1) to the straight line d = | 2K − 1 + K + 10 | K2 + 1 = | 3K + 9 | K2 + 1 ∵ chord length is 8, circle radius r

The linear equation of chord length 8 passing through point a (- 1,10) and cut by circle x2 + y2-4x-2y-20 = 0 is______ .

The circle x2 + y2-4x-2y-20 = 0 is transformed into the standard equation (X-2) 2 + (Y-1) 2 = 25
When the slope of the line is k, the equation of the line is Y-10 = K (x + 1), that is, kx-y + K + 10 = 0
The distance from the center of a circle (2, 1) to the straight line d = | 2K − 1 + K + 10|
k2+1＝|3k+9|
k2+1
And ∵ chord length is 8, circle radius r = 5, ᙽ chord center distance d = 3,
∴|3k+9|
k2+1＝3，
∴k＝−4
Three
The linear equation is 4x + 3y-26 = 0
When the slope of the line does not exist, the equation is x + 1 = 0, and the distance from the center of the circle (2,1) to the line is 3, and the chord length is 8
To sum up, the equation of the straight line is 4x + 3y-26 = 0 or x = - 1
So the answer is: 4x + 3y-26 = 0 or x = - 1

The equations of the line with the longest chord length and the shortest chord length are obtained respectively through the point a (1, - 2) and cut by the circle x ^ 2 + y ^ 2-4x + 2Y = 0

The standard equation of the circle x ^ 2 + y ^ 2-4x + 2Y = 0 is
(x-2)^2+(y+1)^2=5
The center of the circle is: (2, - 1)
Easy to judge: a (1, - 2) is in the circle
(1) The longest chord is the diameter,
In this case, the slope of the line k = (- 2 + 1) / (1-2) = 1
The linear equation is: y = x-3
(2) For the shortest chord, the straight line is perpendicular to the diameter passing through point a,
At this time, the slope of the line k = - 1
The linear equation is: y = - x + 1

Given a point a (4,2) in the circle x + y-4x + 6y-12 = 0, find the equation of the line L where the chord with the midpoint of a is located?

Center B (2, - 3) KAB = 1 / 2 KL = - 2 y - (- 2) = - 2 * (x-4) y = - 2x + 6

Given the square of circle x + the square of Y - 4x + 6y-12 = 0, a point a (4, - 2) is known to solve the linear equation of chord l with point a as the midpoint

Center B (2, - 3)
KAB=1/2
KL=-2
Y-(-2)=-2*(X-4)
Y=-2X+6

In the known circle x ^ 2 + y ^ 2-4x + 6y-12 = 0, the trajectory equation of chord midpoint with length 8 is (X-2) ^ 2 + (y + 3) ^ 2 = 9 In the known circle x ^ 2 + y ^ 2-4x + 6y-12 = 0, the trajectory equation of chord midpoint with length 8 is (X-2) ^ 2 + (y + 3) ^ 2 = 9

It is proved that the equation of circle is (X-2) ^ 2 + (y + 3) ^ 2 = 5
The coordinates of the center of the circle are (2, - 3)
The chord center distance of a string of 8 is always equal to 3
The trajectory equation of chord midpoint with length 8 is (X-2) ^ 2 + (y + 3) ^ 2 = 9

Given the equation x Λ 2-4x + y Λ 2-6y of a circle, then among the strings passing through point (4,3), the linear equation with the longest chord is? Shortest? Please talk about

First, the standard equation (X-2) ^ 2 + (Y-3) ^ 2 = 13
Draw a circle with (2,3) as the center and √ 13 as the radius
It can be seen from the figure that the longest chord passing through the point (4,3) is the diameter. The linear equation is: y = 3
The shortest chord is perpendicular to the longest chord. The linear equation is: x = 4

It is known that two circles x2 + y2-10x-10y = 0, X2 + Y2 + 6x-2y-40 = 0, Find (1) the equation of the line where their common chord lies; (2) the common chord length

（1）x2+y2-10x-10y=0，①；x2+y2+6x-2y-40=0②；
② - 1: 2x + Y-5 = 0 is the equation of the line where the common chord is located;
(2) The chord center distance is: | 10 + 5 − 5|
22+12=
Half the length of the string is 20
50−20＝
30, the common chord length is 2
Thirty

Two circles x2 + y2-10x-10y = 0, X2 + Y2 + 6x-2y-40 = 0, the common chord length is___ .

The standard equations of two circles x2 + y2-10x-10y = 0, X2 + Y2 + 6x-2y-40 = 0 are respectively (X-5) 2 + (Y-5) 2 = 50, (x + 3) 2 + (Y-1) 2 = 50, so the centers of the two circles are a (5, 5), B (- 3, 1); the radii are 50 and 50

It is known that two circles x2 + y2-10x-10y = 0, X2 + Y2 + 6x-2y-40 = 0, Find (1) the equation of the line where their common chord lies; (2) the common chord length

（1）x2+y2-10x-10y=0，①；x2+y2+6x-2y-40=0②；
② - 1: 2x + Y-5 = 0 is the equation of the line where the common chord is located;
(2) The chord center distance is: | 10 + 5 − 5|
22+12=
Half the length of the string is 20
50−20＝
30, the common chord length is 2
Thirty