The chord length of the straight line kx-y + 6 = 0 cut by the circle x2 + y2 = 25 is 8, and the value of K is obtained

The chord length of the straight line kx-y + 6 = 0 cut by the circle x2 + y2 = 25 is 8, and the value of K is obtained

The chord length of the straight line kx-y + 6 = 0 cut by circle x2 + y2 = 25 is 8, the distance between chord centers is 52 − 42 = 3, and the solution is k = ± 3

It is known that circle O: x2 + y2 = 1 and line L: y = KX + 2 (1) when k = 2, find the chord length of line L cut by circle O; (2) when line L is tangent to circle O, find the value of K

(1) When k = 2, the equation of line L is: 2x-y + 2 = 0 ------ (1 point) let the two intersections of line L and circle o be a and B passing through the center of circle O (0,0) as OD ⊥ AB at point D, then od = | 2 × 0-0 + 2 | 22 + (- 1) 2 = 25 ------ (3 points) | ab | = 2ad = 212 - (25) 2 = 255 ------ (5 points) (2

The chord length of line y = KX cut by circle x2 + y2 = 2 is ()
A. 4B. 2C. 2D. 22

From the circle equation, we can get: Center of circle (0, 0), radius r = 2, ∵ the distance between center of circle and straight line y = KX d = 0, ∵ the chord length of straight line cut by circle is 2r2 − D2 = 22

The line | is parallel to the line x + y = 5, and is tangent to the square of the circle x plus the square of Y, which is equal to eight

Let the straight line y + X + B = O, use the distance from the center of the circle to the straight line = radius to find B. | B | / root 2 = 2 times root 2, then B = ± 4, so the straight line is y + × + 4 = 0 or y + x-4 = 0

4-x & # 178; / X & # 178; - 4x + 4 reductive results

=（2-x）（2+x）/（2-x）²
=（2+x）/（2-x）

What is the x-square + 4x + 3 / 3 x-square-x-2 fraction

=(x + 3) (x + 1) (X-2)
=(x + 3) of (X-2)

X-square + 4x + 4 -------- x-square-4, which is the fractional line

Original = (X & # 178; + 4x + 4) / (X & # 178; - 4)
=(x+2)²/[(x+2)(x-2)]
=(x+2)/(x-2)

3 (x-1) (X-2) - 3x (x + 3) (whole process)

3(x-1)(x-2)-3x(x+3)
=3（x^2-3x+2)-3x(x+3)
=3x^2-9x+6-3x^2-9x
=6-18x

A score is scored once with 3, twice with 2, and three fifths. What's the original score? (please write the process.)

（3*2*2*3）/（3*2*2*5）=36/60
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Try to compare the size of (x-1) (x-3) and x ^ 2 + 3x + 3

(x-1) (x-3) = x ^ 2-4x + 3, minus x ^ 2 + 3x + 3 to get - 7x
xx^2+3x+3
x=0,（x-1）(x-3)=x^2+3x+3
x>0,（x-1）(x-3)