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It is proved that no matter what the value of K is, there are two intersections between the line L: kx-y-4k + 2y-3 = 0 and the circle C: X & # 178; + Y & # 178; - 6x-8y + 21 = 0 It is proved that no matter what the value of K is, there are two intersections between the line L: kx-y-4k + 2y-3 = 0 and the circle C: X & # 178; + Y & # 178; - 6x-8y + 21 = 0
Kx-y-4k + 2y-3 = 0 is reduced to - K (x-4) = Y-3
So the straight line passes through the point (4,3)
The center of circle C is (3,4) and the radius is 2
The distance between points (4,3) and (3,4) is root 2, less than 2
So the point (4,3) is in the circle, so the line and the circle intersect at 2 points
We know that the circle x ^ 2 + y ^ 2-2x-2y + 1 = 0, the line y = KX
It is known that the circle x ^ 2 + y ^ 2-2x-2y + 1 = 0, the line y = KX, and the intersection of the line and the circle C is the point P, Q;
We also know the point m (0, b), and MP ⊥ MQ
① When B = 1, find K
② When B is (1,3 / 2), the range of K is obtained
Elder brother and elder sister, thank you on your knees
Let P (x1, kx1) Q (X2, kx2) - according to the linear equation, the vectors MP (x1, kx1-b), MQ (X2, kx2-b) are vertical, and X1 * x2 + (kx1-b) * (kx2-b) = 0. Replace the value of B and simplify it to: (K ^ 2 + 1) * X1 * x2-k (x1 + x2) + 1 = 0
Two real roots of the equation x & # 178; + (M-3) x + M = 0, X &;, X &;, and X &; ≤ X &;, if &; < m < 1,
A X &; < 0 and X &; > 0
B 0＜x₁≤x₂＜2
C X &; ∈ [0,2] and X &; do not belong to [0,2]
D 0＜x₁＜1＜x₂＜2
Ask for detailed explanation ([_ ☆)
I don't understand the answer of C. I can count between x1x2: 1 and 2 / 3
X1 + x2: between 6-3 and 7-3
X2-x1: between 0 and 5 / 3 or between 0 and - 5 / 3, but the latter is excluded
(the endpoint method used above does not include two extreme values)
So choose D
If the two roots of the equation x & # 178; + 8x-4 = 0 are X & # 8321;, X & # 8322;, then the value of 1 / X & # 8321; + 1 / X & # 8322; is?
x1+x2=-8
x1x2=-4
1/x₁+1/x₂
=(x1+x2)/x1x2
=-8/(-4)
=2
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- 11. For the function y = 2x, when it is less than or equal to 2, the value range of Y is y____ 1 or Y_____ .
- 12. The function y = - 2x ^ 2-4x + 3 is known. When the independent variable x is in the following value range, calculate the maximum or minimum value of the function respectively, and calculate the value of the function And find the value of the corresponding independent variable x when the function takes the maximum or minimum value
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