What about vector translation scalar shift Given the straight line L: x-2y + M = 0, the straight line L1 and circle (X-2) obtained by translating according to the vector a = (2, - 3) ²+ (y-1) ²= 5 tangent, m value?

What about vector translation scalar shift Given the straight line L: x-2y + M = 0, the straight line L1 and circle (X-2) obtained by translating according to the vector a = (2, - 3) ²+ (y-1) ²= 5 tangent, m value?

If the point (x, y) is on the straight line L1, its corresponding point before translation is (a, b), then (a, b) + (2, - 3) = (x, y), so a = X-2, B = y + 3, and (a, b) is on the straight line L: x-2y + M = 0, so (X-2) - 2 (y + 3) + M = 0, that is, x-2y + M-8 = 0, so the equation of straight line L1 is x-2y + M-8 = 0, because L1 and circle (X-2) ²+ (y-1) ²= 5...

What does a vector translation mean? How l a translation method? Formula? For example, it is known that a (3,7), B (5,2), after translating the vector AB according to the vector a = (1,2), the coordinates of the obtained vector are? What is translation by a vector? How to move? According to which point and which path? Can you describe it for me? You'd better draw a picture

A (3,7), B (5,2), ab = (2, - 5), a = (1,2) let the vector AB translate according to a and reach a'B ', a' (x1, Y1), B '(X2, Y2)
AA '= a (x1-3, y1-7) = (1,2) x1-3 = 1 and y1-7 = 2 so X1 = 4, Y1 = 9 a' (4,9)
BB '= a (x2-5, y2-2) = (1,2) x2-5 = 1 and y2-2 = 2 so x2 = 6 y2 = 4 B' (6,4)
A'B'=(2,-5)
Translating a vector does not change the direction or size, but changes the coordinates of the two endpoints, so a and B translate to a 'and B' respectively, but the coordinates of vector a'B 'still = the coordinates of vector ab
If you draw a picture in the coordinate system, you will understand

Please explain the problem of translation by vector clearly If the image with F (x) = x ^ 2 + 4x + 5 is translated by a as the image with y = x ^ 2, then a= That is, to translate by vector is to give X-H, Y-K?

The following describes the general method (which is also the method required by the textbook)
Let a = (h, K), the coordinates after translation (x1, Y1),
Then x = x1-h and y = y1-k, substitute y = x ^ 2 + 4x + 5 to get
y1-k=(x1-h) ²+ 4 (x1-h) + 5, finishing:
y1=(x1) ²+ 2(2-h)x1+5+k,
‡ 2-h = 0 and 5 + k = 0,
So h = 2, k = - 5
‡ vector a = (2, - 5)

Shift the image of function y = sin2x to the right π 4 units, and then translate 1 unit upward. The functional analytical formula of the obtained image is () A. y=2cos2x B. y=2sin2x C. y=1+sin（2x+π 4） D. y=cos2x

Shift the image of function y = sin2x to the right π
Four units, the function y = sin2 (x - π
4) = - cos2x,
Then translate the obtained image upward by 1 unit, and the analytical function of the obtained image is y = - cos2x + 1 = 2sin2x,
Therefore: B

The image f of function y = sin2x, after translating the vector (- 1,1), obtains the image f ', then the function analytical formula of image f' is

F′=sin2（x+1）+1

Fill in the blanks: 1. If the length of the lower bottom of the trapezoid is x, the length of the upper bottom is 1 / 3 of the length of the lower bottom, the height is y and the area is 60, the analytical formula of the function of Y and X is ___ (regardless of the value range of x) 2. Within a certain range, the demand for an article is inversely proportional to the supply. It is now known that when the demand is 500 tons, the market supply is 10000 tons, and when the market supply is 16000 tons, the demand is ___

1、0.5*（4/3x)*y=60
2、312.5