The chord length of the straight line kx-y + 6 = 0 cut by the circle x ^ 2 + y ^ 2 ^ = 25 is 8? The radius of the circle is 5 The straight line kx-y + 6 = 0 is cut by the circle x ^ 2 + y ^ 2 = 25, and the chord length is 8 So the distance from the center of the circle to the straight line = root (5 ^ 2-4 ^ 2) So 6 / radical (k ^ 2 + 1) = 3 k^2+1=4 K = radical 3 or K = - radical 3 So the distance from the center of the circle to the straight line = root sign (5 ^ 2-4 ^ 2). How does 4 ^ 2 come from here?

The chord length of the straight line kx-y + 6 = 0 cut by the circle x ^ 2 + y ^ 2 ^ = 25 is 8? The radius of the circle is 5 The straight line kx-y + 6 = 0 is cut by the circle x ^ 2 + y ^ 2 = 25, and the chord length is 8 So the distance from the center of the circle to the straight line = root (5 ^ 2-4 ^ 2) So 6 / radical (k ^ 2 + 1) = 3 k^2+1=4 K = radical 3 or K = - radical 3 So the distance from the center of the circle to the straight line = root sign (5 ^ 2-4 ^ 2). How does 4 ^ 2 come from here?

The radius of the circle is 5
So, half the length of the string, the radius and the distance from the center of the circle to the string form a right triangle, which is known by the Pythagorean theorem
So the distance from the center of the circle to the straight line = root (5 ^ 2-4 ^ 2)

If the maximum chord length of a point P (- 1,0) in the circle x ^ 2 + y ^ 2-4x + 6y-12 = 0 is l and the minimum chord length is l, then L-L = ()?
The answer is 10-2 root 7

(X-2) ^ 2 + (y + 3) ^ 2 = 25, so the center (2, - 3), radius is 5
The maximum chord length is the diameter through the point, and the minimum chord length is the chord perpendicular to the diameter
Then l = 10,
|OP | = [(- 1-2) ^ 2 + (- 3) ^ 2] ^ (1 / 2) = 3 radical 2
Minimum chord length L = 2 * [5 * 5 - | op | ^ 2]] ^ (1 / 2) = 2 * (7) ^ (1 / 2)
L-L = 10-2 radical 7

If there are two points m and N on the number axis, and Mn = root 5, the number represented by point n is root 7, then the number represented by point m is root 7___ Mn is the distance between two points

7 ± root 5

The equation of parabola can be obtained by crossing the straight line with 45 degree inclination angle and parabola y = ax ＾ 2 with B, C and BC being the equal proportion median of AB and AC through the fixed point a (- 2, - 1)
How to work out the equation of a straight line and how to use the condition of equal proportion middle term

a=1/5
The linear equation is y = x + 1
Simultaneous equations
We get AX2 = x + 1
Find out the two roots of the equation, that is, the abscissa of the intersection of the straight line and the parabola
They are (1 + 4a) / 2a and (1 + 4a) / 2A under 1-radical respectively
Then, by using the middle term of the equal ratio, the length of AB, AC and BC can be obtained without calculation here
(because their length is equal to the difference between the abscissa of root 2 ~ the angle is 45 ~ after both sides are multiplied, they become x 2, which can be seen.)
It is calculated that XAB (the difference of abscissa) is (1 + 4a) / 2A under 3-radical
XAC is (1 + 4a) / 2A under 3 + radical
XBC is (1 + 4A under radical) / A
Using XBC ^ 2 = XAC × XAB
A = 1 / 5 is obtained

A set a, B with three elements, a = {2, x, y}, B = {2x, 2, 2Y}, and a = B, find the value of X, y

If x = 2x, y = 2Y, then x = y = 0, there are three elements in the set;
If x = 2Y, y = 2x, the solution is also 0,
So there is no solution

Parabola y = 2x ^ 2, fixed point P (1,2), a, B are two moving points on parabola, and the slopes of PA and Pb are non-zero and opposite to each other, so the slope of AB can be obtained

Parabola C: y = 2x square let: a (x1, Y1), B (X2, Y2) because: P, a, B are all on C, and kPa = - KPB, so: Y1 = 2x1 square, y2 = 2x2 square (2-y1) / (1-x1) = - (2-y2) / (1-x2) substitute the first two formulas into the third formula: simplify to: X1 + x2 = - 2, so: KAB = (y1-y2) / (x1-x2) = [2 (x1-x2) (...)

Solution set of equation x ^ 2 + 2Y ^ 2-2x + 8y + 9 = 0

x^2+2y^2-2x+8y+9=0
(x^2-2x+1)+2(y^2+4y+4)=0
(x-1)^2+2(y+2)^2=0
x-1=0
y+2=0
x=1
y=-2

Given the circle C: x ^ 2 + y ^ 2 + 4x-3 = 0 (1), try to prove: when m is any real number, the line L: (M + 2) x + (m-1) y + 2m + 1 = 0 must intersect the circle C

x²+y²+4x-3=0
(x+2)²+y²=7
Let x = - 1, y = - 1
(-1+2)²+(-1)²=2

If we take any two different elements x and Y from the set M = {x, X is less than or equal to 100, X belongs to n *} and satisfy the condition of X + y = n
If from set
M = {x is less than or equal to 100, X belongs to n *}
If the probability of X + y = n is 1 / 150, then the maximum value of XY is ()
A.4488
B.4355
C.4623
D.4970

If there are 1,2 and. 100 numbers in M, then there are 100 * 99 results for x + y, and we can get the results of X + y = n. if M is set as m, then M / 9900 = 1 / 150  M = 66, that is to say, we can get 66 results for x + y = n, that is, n = 67 (x = 1,2,. 66) or n = 68 (x = 1,2,. 67, where x = 34 is not good), or n = 135 (x = 100,99,. 35) or n = 134 (x = 100,99,. 34)

The linear equation passing through point (- 3,4) and tangent to circle x square + y square-2x-2y-23 = 0

Deformation of circular equation: (x-1) ^ 2 + (Y-1) ^ 2 = 5 ^ 2
Radius of center C (1,1) r = 5
Let the linear equation: y-4 = K (x + 3) = > kx-y + 3K + 4 = 0
If a line is tangent to a circle, the distance from the center of the circle to the line is equal to 5
|k-1+3k+4|/√(k²+1²)=5 => (4k+3)²=25(k²+1) => 16k²+24k+9=25k²+25
9k²-24k+16=0 ∴k=4/3
Tangent equation: 4x / 3-y + 3 * 4 / 3 + 4 = 0 = > 4x-3y + 24 = 0