If the common chord length of circle x2 + y2 = 4 and circle x2 + Y2 + 2ay-6 = 0 (a > 0) is 2 3, then a is equal to () A. 1 B. Two C. Three D. 2

It is known that the radius of x2 + Y2 + 2ay-6 = 0 is
6 + A2, the center coordinate is (0, - a)
The radius of circle x2 + y2 = 4 is 2, and the coordinates of its center are (0, 0)
∵ the length of the common chord of circle x2 + y2 = 4 and circle x2 + Y2 + 2ay-6 = 0 (a > 0) is 2
3，
Then the distance from the center (0, 0) to the common chord is 1
The distance from the center (0, - a) to the common chord is 1 + a
It can be seen from the figure that 6 + a2 - (a + 1) 2=（
3) A = 1
So choose a

The chord of circle x2 + Y2 + 2x-4y-164 = 0 is made by crossing point a (11,2), where the chord length is the common () A. 16 B. 17 C. 32 D、 34

The standard equation of circle is: (x + 1) 2 + (Y-2) 2 = 132, Center (- 1,2), radius r = 13. The shortest chord length of point a (11,2) is 10, the longest chord length is 26, (there is only one chord respectively) and the length is 11,12 There are 2 + 2 × 15 = 32 chord lengths of integers
Therefore, C

The chord of circle x2 + Y2 + 2x-4y-164 = 0 is made by crossing point a (11,2), where the chord length is the common () A. 16 B. 17 C. 32 D、 34

How many chords of the circle x ^ 2 + y ^ 2 + 2x-4y-164 = 0 are made by crossing the point (11,2)? The center coordinates (- 1,2) and radius 13 can be solved. How to know the number of chords with integer length?

The circle x2 + Y2 + 2x-4y-164 = 0, i.e. (x + 1) ^ 2 + (Y-2) ^ 2 = 13 ^ 2, so point a is inside the circle. The distance from the center of the circle (- 1,2) to point a = 12, so the minimum distance of the chord passing through point a = 2 × (13 ^ 2-12 ^ 2) ^ 0.5 = 10. The maximum value through point a = diameter = 26, so the maximum value of chord = 26, the minimum value = 10, and the chord length is 11,12 ...

Given two circles x ^ 2 + y ^ 2-2x + 10y-24 = 0 and x ^ 2 + y ^ 2 + 2x + 2y-8 = 0 (1) try to judge the position relationship between the two circles; (2) find the linear equation where the common chord lies (3) Find the length of the common chord

There are two solutions to the simultaneous equation, one is tangent, and the other is separation. (1) - (2) - 4x + 18y-16 = 0, x = (9y-8) / 2 into (1), we get (9y-8) ^ 2 / 4 + y ^ 2 - (9y-8) + 10y-24 = 0, y = 0, y = 70 / 17, x = (9y-8) / 2 x = - 4, x = 247 / 17

Given that the straight line x + 3Y + 1 = 0 and the circle x2 + y2-2x-3 = 0 intersect at two points a and B, then the equation of the vertical bisector of segment AB is______ .

The circular equation is transformed into the standard equation and the result is: (x-1) 2 + y2 = 4,
The coordinates of the center of the circle are (1, 0),
∵ the slope of AB equation x + 3Y + 1 = 0 is - 1
3，
The slope of the vertical bisector equation of line AB is 3,
Then the equation of the vertical bisector of line AB is y-0 = 3 (x-1),
That is, 3x-y-3 = 0
So the answer is: 3x-y-3 = 0

Let the straight line 2x + 3Y + 1 = 0 and the circle x ^ + y ^ - 2x-3 = 0 intersect at a and B. then the equation of the vertical bisector of chord AB is What I mean is that the simultaneous equations can solve a and B, and then the slope of the midpoint can also be obtained by knowing; but how to solve the simultaneous equations

The slope of AB vertical bisector can be calculated
There's a better way
AB vertical bisector is passing through the center (0,1)
Just bring these two into the solution

Let the straight line 2x + 3Y + 1 = 0 and the circle x2 + y2-2x-3 = 0 intersect at points a and B, then the vertical bisector equation of chord AB is______ .

Let the straight line 2x + 3Y + 1 = 0 and the circle x square + y square - 2x + 3 = 0. Intersect at A. B. find the equation of the line where the perpendicular line of string AB lies

The vertical line of AB is a straight line passing through the center of a circle and perpendicular to ab,
From 2x + 3Y + 1 = 0, the slope of line AB is k AB = - 2 / 3, so the slope of straight line is k = 3 / 2;
From x ^ 2 + y ^ 2-2x + 3 = 0, the center (1,0) is obtained,
Therefore, according to the point slant formula, we can get the equation of AB as y-0 = 3 / 2 * (x-1),
3 x - 2 y - 3 = 0

Let the straight line 2x + 3Y + 1 = 0 and the circle x ^ + y ^ - 2x-3 = 0 intersect at points a and B, and find the vertical bisector equation of chord ab

The center of circle C (1,0), the slope of straight line is - 2 / 3, the slope of perpendicular line of AB is 3 / 2, equation y = (3 / 2) (x-1)

If the common chord length of circle x2 + y2 = 4 and circle x2 + Y2 + 2ay-6 = 0 (a > 0) is 2 3, then a is equal to () A. 1 B. Two C. Three D. 2