Set the coordinates of the fixed point m (- 3,4), the moving point n moves on the circle x2 + y2 = 4, and make the parallelogram MONP with OM and on as two sides to find the trajectory equation of the point P

Set the coordinates of the fixed point m (- 3,4), the moving point n moves on the circle x2 + y2 = 4, and make the parallelogram MONP with OM and on as two sides to find the trajectory equation of the point P

Vector MP = vector on
N(x1,y1)
P(x,y)
x+3=x1;y-4=y1
Put it in, get it
(x+3)^2+(y-4)^2=4
When n is on the straight line OM, it is infeasible (± 6 / 5, ± 8 / 5)
x+3≠±6/5,
X ≠ - 9 / 5 and X ≠ - 21 / 5
In conclusion, the trajectory equation of P is
(x + 3) ^ 2 + (y-4) ^ 2 = 4, X ≠ - 9 / 5 and X ≠ - 21 / 5

The line L passing through the origin and the circle x ^ 2 + y ^ 2-6x-4y + 9 = 0 intersect at two different points a and B. what is the trajectory equation for finding the midpoint m of line segment AB?

Let y = KX ①, a (x1, Y1) B (X2, Y2), m (x, y) circle O: (x-3) & sup2; + (Y-2) & sup2; = 4 ② ②: (K & sup2; + 1) x & sup2; - (6 + 4K) x + 9 = 0x1 + x2 = 2x = (6 + 4K) / (K & sup2; + 1) ③, Y1 + y2 = 2Y = K (6 + 4K) / (K & sup2; + 1) ④ om ⊥ AB: (y2-y1) / (x2-x1) * (Y-2) / (x-3) = - 1

Mathematics application problem grade 4
There are 100 rooms in a hotel. During dinner hours, each room is 100 yuan, which can be rented out. If each room is increased by 20 yuan, 10 rooms will be reduced
1. If the charge of each room is increased by X, the income of each room is Y1 yuan, but it will reduce the rental of Y2 rooms. Write the relationship between Y1 and Y2 in X respectively
2. In order to make less investment and more profit, after each room is increased by X Yuan, the total down payment of the hotel owner is y yuan every day. Write the functional relationship between Y and X

1.y1=100+x
y2=10×x/20=x/2
2. y=y1×（100-y2）
=（100+x）（100-x/2）
=-x²/2+50x+10000

Draw the largest circle in a square with a circumference of 16 cm. The area of the circle is ()
A. 50.24 square centimeter B. 16 square centimeter C. 12.56 square centimeter

The radius of the circle: 16 △ 4 △ 2 = 2 (CM), the area of the circle: 3.14 × 22 = 12.56 (square cm), answer: the area of the square is 12.56 square cm

If the square of (a + b) is known to be 19, and the square of (a-b) is known to be 27, find the value of ab

We know that the square of (a + b) is 19,
a^2+2ab+b^2=19-----(1)
Square of (a-b) = 27
a^2-2ab+b^2=27-----(2)
From (1) - (2)
4ab=19-27=-8
ab=-2

Three practical questions
1. The garden has a good harvest of tomatoes. When three eighths of my staff are full of one basket, it is 24 kg more. When the rest of my staff are finished, it is just 6 baskets full. How many kilos of tomatoes should I collect?
2. The number of absentees in a class is one ninth of the attendance, and then a classmate goes to the meeting. In this way, the number of absentees accounts for three twenty-two percent of the attendance. It is known that the number of boys in this class is one twelfth more than that of girls. How many boys and girls are there in this class?
3. There are 84 people in class A and class B. There are 58 people in class A and class B. how many people are there in each class?

1.
Five eighths of all, just six frames full
One eighth of all, 6 / 5 frames
Three eighths of the total are 18 / 5 boxes, which are filled with 3 boxes and 3 / 5 baskets
All 9 baskets and 3 / 5 baskets
According to the title, 3 / 5 basket is 24 kg
A full basket is 40 kg
Total tomatoes 9 * 40 + 24 = 384kg
two
It should be noted that they are not in class now, no matter they are in a meeting or something, they are not in class anyway,
Later, another one went to class, which was counted as the absent one,
So Y-1 = 3 / 22 (x + 1), the combined solution of the two equations is y = 5, so x = 45
Then, let m be male and n be female, and 1 / 12n + n be male,
So 13 / 12n + n = 50,
N = 24, M = 26,
There are 26 boys and 24 girls
three
There are two ways:
(1) Let class a be x and class B be y. then the equation is
X+Y=84
5/8X+3/4Y=58
The solution is as follows
X=40
Y=44
(2) Let x people in class A, then (84-x) people in class B
5/8X+3/4(84-X)=58
The solution is as follows
There are 40 in class A and 44 in class B

The total area of 8 square boards of the same size is 18 square meters, so the length of each side of the board is

From 18 / 8 = 9 / 4, we can know that the area of each small square is four ninths, and four ninths of the root sign is equal to three-thirds, so the length of each side of the board is three-thirds

I always heard that how many light years is the planet so and so from the earth? How do those astronomers measure it? Do they need to measure 50 light years from the earth

A laser is emitted to measure the distance of a closer star, and then a computer is used to analyze the distance on the star map according to the satellite photos, so as to estimate the distance of the farther star

Practical problems of density in grade two of junior high school
If 500ml of dilute sulfuric acid with a density of 1.2g/cm ^ 3 is prepared, how many ml of concentrated sulfuric acid need to be mixed with water? The volume does not change during the mixing process. (P concentrated sulfuric acid = 1.8g / cm ^ 3) (if the sign of density cannot be printed, use p instead)

If the volume of concentrated sulfuric acid is V, then
ρ concentrated sulfuric acid V + ρ water (500-V) = 500 * 1.2
Namely: 1.8V + 1.0 (500-V) = 600
It can be concluded that the volume of concentrated sulfuric acid is
V=125ml

A cylinder with a circumference of 12.56 cm on the bottom is cut into several equal parts along the radius of the bottom to form an approximate cuboid. The surface area is increased by 20 square centimeters. What is the volume of the original cylinder?

The height of the cylinder: 20 △ 2 ^ (12.56 △ 3.14 ^) 2, = 10 △ 2, = 5 (CM); 3.14 × (12.56 △ 3.14 ^) 2 × 5, = 3.14 × 4 × 5, = 3.14 × 20, = 62.8 (CC); a: the original volume of the cylinder is 62.8 cubic cm