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If there are two different intersections between the line y = KX + 2 and the circle (X-2) + (Y-3) = 1, find the value range of K
There are two different points of intersection, that is, the distance from the center of the circle to the straight line is less than the radius. If it is equal to, it is tangent and an intersection
So the distance from (2,3) to the straight line kx-y + 2 = 0 is k ^ 2 + 1 under | 2k-3 + 2 | / following sign
Why is it wrong to say that "uniform velocity linear motion is a linear motion in which the displacement changes uniformly with time"
I know the concept of uniform variable speed linear motion, but the increment of displacement in any period of equal adjacent time is constant. For example, in uniform acceleration linear motion, the displacement in the later period is a constant amount more than that in the previous period, that is, the increment is the same. How can it not be uniform? Add a constant amount on the basis of the original increase,
The displacement increment of two adjacent segments is constant, but the total displacement increment of each segment is different. Therefore, it should be said that "uniform linear motion is a linear motion in which the displacement changes uniformly with time", rather than uniform velocity. "Uniform velocity linear motion is a linear motion in which the velocity changes uniformly with time", rather than displacement
Given that hyperbola y = 3x and straight line y = KX + 2 intersect point a (x1, Y1) and point B (X2, Y2), and X12 + X22 = 10, find the value of K
From y = KX + 2Y = 3x, it is obtained that 3x = KX + 2, kx2 + 2x-3 = 0. Therefore, X12 + X22 = (x1 + x2) 2-2x1 · x2 = 4k2 + 6K = 10. 5k2-3k-2 = 0, K1 = 1 or K2 = - 25. (4 points) and △ = 4 + 12K ＞ 0, that is, K ＞ - 13, so the value of K is 1. (6 points)
When an object moves in a straight line, if the displacements that change in the same time are equal, then the motion of the object is a uniform linear motion. Is that right
It can go back for a while and then move forward. Or does linear motion still keep the same displacement in the same time, but it's not uniform linear motion?
Hyperbola y = 3 / x, straight line y = KX + 2, they intersect at a (x1, Y1), B (X2, Y2), and the sum of the square of X1 and the square of X2 is equal to 10, find the value of K
Substituting y = 3 / x into the equation y = KX + 2, eliminating Y3 / x = KX + 2kx ^ 2 + 2x-3 = 0x1, X2 is the two roots of the equation, △ = 4 + 12K > 0, k > - 1 / 3. According to Weida's theorem, X1 + x2 = - 2 / kx1x2 = - 3 / K (x1) ^ 2 + (x2) ^ 2 = (x1 + x2) ^ 2-2x1x2 = 4 / K ^ 2 + 6 / k = 105K ^ 2-3k-2 = 0 (5K + 2) (k-1) = 0k = 1 or K = - 2 / 5
The following statement about uniform variable speed linear motion is correct ()
A. The change of displacement in the same time is the same B. the change of velocity in the same time is the same C. The change of acceleration in the same time is the same and not zero D. the change rate of velocity at any time is the same
A. In the case of uniform variable speed linear motion, the change of displacement in the same "continuous" time is the same. If it is not "continuous" time, it may not be the same. Therefore, a is wrong. B. uniform variable speed linear motion speed changes uniformly with time, then the change of speed in the same time is the same. Therefore, B is correct. C. uniform variable speed linear motion acceleration does not change. Therefore, C is wrong. D. the change rate of speed is equal to plus Speed, uniform speed, linear motion acceleration unchanged. So D is correct. So BD is selected
Given that the line y = KX (k > 0) and hyperbola y = 3x intersect at two points a (x1, Y1), B (X2, Y2), then the value of x1y2 + x2y1 is ()
A. -6B. -9C. 0D. 9
∵ points a (x1, Y1) and B (X2, Y2) are points on hyperbola y = 3x ∵ x1 · Y1 = x2 · y2 = 3 ①, ∵ straight line y = KX (k > 0) intersects hyperbola y = 3x at two points a (x1, Y1), B (X2, Y2), ∵ X1 = - X2, Y1 = - Y2 ②, ∵ primitive = - x1y1-x2y2 = - 3-3 = - 6
The car starts to do uniform acceleration motion from standstill, the acceleration is the square of 5m / s, and the speed should reach 40m / s?
From v = at, we can get 40 = 5T, t = 8, the car does the linear motion of uniform acceleration with zero initial velocity, s = (1 / 2) (a) (T) ^ 2 = 160
As shown in the figure, if the line y = KX (k < 0) and hyperbola y = − 2x intersect at two points a (x1, Y1) and B (X2, Y2), then the value of 3x1y2-8x2y1 is ()
A. -5B. -10C. 5D. 10
∵ a (x1, Y1), B (X2, Y2) hyperbola y = − 2x, ∵ x1y1 = - 2, x2y2 = - 2, ∵ straight line y = KX (k < 0) intersects hyperbola y = − 2x at two points of a (x1, Y1), B (X2, Y2), ∵ X1 = - X2, Y1 = - Y2, ∵ x1y2 = - x1y1, x2y1 = - x2y2, ∵ 3x1y2-8x2y1 = - 3x1y1 + 8
A car running at a speed of 12 / s moves in a straight line with uniform speed change when braking. The acceleration is the square of - 6 m / s?
v=at
12=6t
t=2s
s=v0t+1/2at^2
=12*2+1/2*(-6)*4
=12m
RELATED INFORMATIONS
- 1. If the line y = KX (k > 0) and hyperbola y = 4 / X intersect at two points a (x1, Y1) and B (X2, Y2), then the value of 2x1y2-7x2y2
- 2. Prove: no matter what the value of K is, the straight line L: kx-y-4k + 3 = 0 and the curve C: x ^ 2 + y ^ 2-6x-8y + 21 = 0 always have several intersections 1. To make the line intersect the circle, the distance from the center of the circle to the line is | 3k-4-4k + 3 | / (radical K ^ 2 + 1) Radical (1 + 2K / (1 + K ^ 2))
- 3. The position relationship between the square of X + the square of Y - 6x = 0 and the square of circle x + the square of Y - 8y = 0. If they intersect, the common chord length can be obtained,
- 4. It is known that the center of the hyperbola is at the origin, the focal points F 1 and F 2 are on the coordinate axis, the eccentricity is 2 ^ 1 / 2 and passes through the point (4, - 10 ^ 1 / 2) It is known that the center of the hyperbola is at the origin, the focus F 1 and F 2 are on the coordinate axis, the eccentricity is 2 ^ 1 / 2 and passes through the point (4, - 10 ^ 1 / 2). Find the hyperbolic equation; if the point m (3, M) is on the hyperbola, find out: the point m is on the circle with the diameter of F 1F 2; find out the area of the triangle f 1m F 2
- 5. The coordinates of the focus are (- 6,0), (6,0) and the standard equation of hyperbola passing through point a (- 5,2)
- 6. Some problems on the standard equation of hyperbola 1. The focal coordinates are (0, - 6), (0,6) and (2, - 5) respectively 2. Eccentricity e = 4 / 3, imaginary axis length is 2 times root 7, focus on Y axis 3. The focal length is 10, the distance between two vertices is 6, and the vertex is on the X axis
- 7. Given that K is a real number, if the focal length of hyperbola X2K − 5 + Y22 − | K | = 1 has nothing to do with the value of K, then the value range of K is () A. （-2，0]B. （-2，0）∪（0，2）C. [0，2）D. [-1，0）∪（0，2]
- 8. Let the center of the ellipse be at the origin o, the focus be on the x-axis, the eccentricity be √ 2 / 2, and the sum of the distances between a point P and two focus points on the ellipse be equal to √ 6. Let the center of the ellipse be at the origin o, the focus be on the x-axis, the eccentricity be √ 2 / 2, and the sum of the distances between a point P and two focus points on the ellipse be equal to √ 6. (1) if the straight line x + y + M = 0 intersects the ellipse at two points a and B, and OA ⊥ ob, find the value of M?
- 9. It is known that the center of the ellipse is at the origin, the focus is on the y-axis, the focal length is 4, and the eccentricity is 2 / 3. Suppose that the focus of the ellipse on the positive half axis of the y-axis is m, and a and B are on the ellipse And the vector AB = 2, the vector MB, find the linear equation where the line AB is
- 10. It is known that the center of the ellipse with eccentricity of 4 / 5 is at the origin and the focus is on the x-axis It is known that the center of the ellipse with eccentricity of 4 / 5 is at the origin and the focus is on the x-axis. The hyperbola takes the major axis of the ellipse as the real axis and the minor axis as the imaginary axis. If the focal length of the hyperbola is 2 root sign 34, the equations of the ellipse and hyperbola can be solved
- 11. The left and right fixed points of ellipse C1: x ^ 2 / A ^ 2 + y ^ 2 / 4 = 1 (a is greater than 2) are a and B respectively, and point P is the image of hyperbola C2: x ^ 2 / A ^ 2-y ^ 2 / 4 = 1 in the first quadrant If the area of triangle ACD and triangle PCD is equal, (1) calculate the coordinates of point p; (2) whether the line CD can pass the right focus of ellipse C1, if it can, calculate the value of A. if not, please explain the reason
- 12. How to solve the equation (LNX) ^ 3-1 + x = 0?
- 13. The left and right focus of the hyperbola x2a2 − y2b2 = 1 is F1, F2, P is a point on the hyperbola, satisfying | PF2 | = | F1F2 |, and the straight line Pf1 is tangent to the circle x2 + y2 = A2, then the eccentricity e of the hyperbola is () A. 3B. 233C. 53D. 54
- 14. Point P is a point on the hyperbola x2 / 25-y2 / 9 with F1 and F2 as the focus, and the absolute value of Pf1 = 12, then the absolute value of PF2=
- 15. It is known that the focus of the ellipse x ^ 2 / 4 + y ^ 2 = 1 is F1, F2, and the intersection of the parabola y ^ 2 = PX (P > 0) and the ellipse in the first quadrant is Q, if ∠ f1qf2 = 60 °, (1) Calculate the area of △ f1qf2; (2) Find the equation of this parabola
- 16. Given that - 90 degree is less than X and less than 0 degree, SiNx + cosx = 0.2, find SiNx cosx =?
- 17. F (x) = the maximum of SiNx cosx
- 18. Are there overlaps between infinite discontinuities and oscillatory discontinuities, such as piecewise function x < 0, f (x) = 1 / x, x > 0, f (x) = sin Is there any overlap between infinite discontinuity and oscillation discontinuity For example, when the piecewise function x < 0, f (x) = 1 / x, x > 0, f (x) = sin (1 / x), what is the breakpoint of x = 0?
- 19. F (x) = sin (ω x + φ) (ω is greater than 0, φ is greater than or equal to 0 and less than or equal to π) is even function, and the distance between two adjacent highest points on the image is 2 π It is known that the function f (x) = sin (ω x + φ) (ω greater than 0,0 ≤ φ ≤ π) is even function, and the distance between two adjacent highest points on the image is 2 π 1. Find the analytic expression of F (x) 2. If a belongs to (- π / 3, π / 2), f (a + (π / 3)) = 1 / 3, find the value of sin (2a + (5 π / 3))
- 20. If the sum of the first n terms of the equal ratio sequence {an} is 2N-1, then the sum of the first n terms of the sequence {an ^ 2} is?