The distance from the known moving point m to the fixed point (1,0) is less than the distance from m to the fixed line x = - 2 by 1 (1) Verification: the trajectory of m point is a parabola, and its trajectory equation is obtained; (2) As we all know, if passing through any point P on the circle and making any mutually perpendicular strings PA and Pb, then the string AB must pass through the center of the circle (fixed point). Inspired by this, the following problems are studied: 1. If passing through the vertex o of the parabola in (1) and making any mutually perpendicular strings OA and ob, does the string AB pass through a fixed point? If passing through a fixed point (set as Q), ask for the coordinates of point Q, Research: for parabola y ^ 2 = 2px, is there such a property? Please give a general conclusion and prove it It is known that positive term sequence {an} satisfies: A1 = 2, and an + 1 = (2An) / ((an) + 2) 1. It is known that the sequence {1 / an} is an arithmetic sequence, and the general term formula of the sequence {an} is obtained 2. Let Sn = A1 / 3 + A2 / 4 + A3 / 5 + +(an) / (n + 2). Find SN

The distance from the known moving point m to the fixed point (1,0) is less than the distance from m to the fixed line x = - 2 by 1 (1) Verification: the trajectory of m point is a parabola, and its trajectory equation is obtained; (2) As we all know, if passing through any point P on the circle and making any mutually perpendicular strings PA and Pb, then the string AB must pass through the center of the circle (fixed point). Inspired by this, the following problems are studied: 1. If passing through the vertex o of the parabola in (1) and making any mutually perpendicular strings OA and ob, does the string AB pass through a fixed point? If passing through a fixed point (set as Q), ask for the coordinates of point Q, Research: for parabola y ^ 2 = 2px, is there such a property? Please give a general conclusion and prove it It is known that positive term sequence {an} satisfies: A1 = 2, and an + 1 = (2An) / ((an) + 2) 1. It is known that the sequence {1 / an} is an arithmetic sequence, and the general term formula of the sequence {an} is obtained 2. Let Sn = A1 / 3 + A2 / 4 + A3 / 5 + +(an) / (n + 2). Find SN

Can I ask you the first question? You can directly set the point (x, y) of M, Let f (1,0) use the distance formula between two points to find | MF | + 1 = D, d = x + 2. It's OK to simplify the equation
I'm sorry to keep you waiting for 2 days. This problem is not too easy. The main calculation is too difficult
2) The answer to the first question should be y ^ 2 (the second power of Y) = 4x
1) Let OA: y = KX, OB: y = (- 1 / k) X,
From y = KX, y ^ 2 = 4x, a (4 / x ^ 2,4 / k) is the same as B (4K ^ 2, - 4K)
So the equation of AB is y + 4K = [(4 / K + 4K) / (4 / K ^ 2-4k ^ 2)] (x-4k ^ 2)
That is y + 4K = [1 / (1 / K-K)] (x-4k ^ 2)
Let y = 0, then 4K (1 / K-K) = x-4k ^ 2
So x = 4, the line must pass Q (4,0)
2) Let P (x0, Y0) be a certain point on y ^ 2 = 2px, then Y0 ^ 2 = 2px0
Make perpendicular strings PA, Pb through P
Let a (x1, Y1), B (X2, Y2), then Y1 ^ 2 = 2px1, Y2 ^ 2 = 2px2,
therefore
[(y1-y0)/(x1-x0)]X[(y2-y0)/(x2-x0)]=-1
Then we use X1 = Y1 ^ 2 / 2p to know XO and x2
It is reduced to (Y1 + Y0) (Y2 + Y0) = - 4P ^ 2, that is, y1y2 + Y0 (Y1 + Y2) + Y0 ^ 2 + 4P ^ 2 = 0 (1)
Suppose AB passes through the fixed point Q (a, b), then there is (y1-b) / (x1-a) = (y2-b) / (x2-a). From the above, we know that X1 = Y1 ^ 2 / 2p. Similarly, we can get X2, which is reduced to y1y2-b (Y1 + Y2) + 2PA = 0 (2)
There are one or two formulas, a = 2p + x0, B = - Y0, that is, Q point. Take a good look at it, I'm tired. It's better to write it in a book, so it's easy to understand

It is known that abcd-a1b1c1d1 is a unit cube. Black and white ants start from point a and crawl forward along the edge. Each edge is called the end of a section. The crawling route of white ants is aa1-a1d1, while that of black ants is ab-bb1, They all follow the following rule: the line of the I + 2 segment and the I segment must be a non planar line (where I is a natural number)?

After a careful analysis of the problem, it's actually very simple,
First, we analyze the route of the white ant: aa1-a1d1-d1c1-c1c-cb-ba-aa1,
Similarly, the route of black ant: ab-bb1-b1c1-c1d1-d1d-da-ab is analyzed. Therefore, it also moves with six edges as a cycle
After 2012 = 6 * 335 + 22012, white ants walk to D1, black ants walk to B1, the distance between them is d1b1, d1b1 = root 2

Both a and B ships will stop at a certain berth for 6 hours. Assuming that they arrive at random in a day and night (24 hours), this paper tries to find out the probability that at least one of the two ships must wait when berthing

Let a arrive at x and B arrive at y, then the area composed of all basic events Ω = {(x, y) | 0 ≤ x ≤ 240 ≤ y ≤ 24 & nbsp;} at least one of the two ships must wait for the area composed of basic events a = {(x, y) | 0 ≤ x ≤ 240 ≤ y ≤ 24 | x − y | ≤ 6 when berthing

The perimeter of a cube is 4 / 5 meters. What is its area?
a. 16 / 25 b.c.d

B

The perimeter of a cube is 4 / 5 meters. How many meters is its side? How many square meters is its area?
Yes, yes, it's "square"

(⊙ V ⊙) well, it's very simple
Because it's a square
So the four sides are equal in length
Because the perimeter is 4 / 5 meters
So the length of each side is 4 / 5 divided by 4 = 1 / 5m
So an area of 1 / 5 square is equal to 1 / 25 square meter

The perimeter of a square is 89 meters. What's its area?

A: its area is 481 square meters

Know the total edge length of cube, how to calculate the edge length of cube!

A cuboid has 12 edges. Divide the total edge length of a cube by 12 edges
I'm a sixth grader. I've learned it