Let the focus of the ellipse be F1 (- 1,0) F2 (1,0) line L: x = a ^ 2 intersecting X axis at point a and vector AF1 = 2 vector af2 (1) the equation for finding the ellipse (2) the inclination angle is 3 / 4 π, the line g intersects with the ellipse at different points m, N. if the circle with Mn as diameter passes through F2, the equation for finding the line G is obtained

Vector AF1 = 2 vector af2
∴a^2+1=2(a^2-1)
a^2=3
∵c^2=1
∴b^2=2
The elliptic equation is
x^2/3+y^2/2=1
(2)
The inclination angle is 3 / 4 π line G
Let g: y = - x + B be a straight line
Substitute x ^ 2 / 3 + y ^ 2 / 2 = 1 to get
5x^2-6bx+3b^2-6=0
Circle crossing F2 with Mn as diameter
Ψ vector F2m · vector f2n = 0
Let m (x1, Y1), (X2, Y2)
The vector F2m = (x1-1, Y1)
Vector f2n = (x2-1, Y2)
∴(x1-1)(x2-1)+y1y2=0
∴x1x2-(x1+x2)+1+(-x1+b)(-x2+b)=0
Well organized
2(3b^2-6)/5-(1+b)6b/5+1+b^2=0
5b^2-6b-7=0
b=(3±2√11）/5
The linear equation is
y=-x+(3+2√11)/5
or
y=-x+(3-2√11)/5
For reference only

It is known that the center of the ellipse is at the origin, the two foci f1.f2 are on the x-axis, and pass through the point a (- 4.3) if the vector AF1 multiplied by af2 = 0

Ellipse C1: x2 / 4 + y2 = 1, ellipse C2 takes the major axis of C1 as the minor axis, E1 = E2, O as the origin, and points a and B respectively seek the equation of line AB from C1, C2 to ob = to 2oa
Linear AB equation

（1）a1^2=4 b1^2=1,c1^2=3 e1=√3/2
b2^2=4 e2=e1 a2^2=16,
Equation of ellipse C2:
x^2 /4 +y^2 /16=1
(2) Let a (x1, Y1) B (X2, Y2), OB = 2oa
So x2 = 2x1, y2 = 2y1
A on ellipse C1: X1 ^ 2 / 4 + Y1 ^ 2 = 1
B on ellipse C2: X1 ^ 2 + Y1 ^ 2 / 4 = 1
Therefore, X1 ^ 2 = Y1 ^ 2 = 4 / 5
The solution is X1 = Y1,
Because AB passes through the origin, the equation of line AB is y = X

If we know that x = 3 / 2, then 1: y = X-2, (x is greater than or equal to - 2, less than or equal to - 1), 2: y = the square of X (x is greater than or equal to - 1, less than or equal to 1),
3: Y = - x + 2 (x is greater than or equal to 1 and less than or equal to 2) combined with these three formulas, what is the final value of Y?

It is known from the title that x = 3 / 2 satisfies the condition of X in 3: y = - x + 2 (x is greater than or equal to 1 and less than or equal to 2),
So y is determined by the third condition
So y = - x + 2 = - 3 / 2 + 2 = 1 / 2
That is, the final value of Y is 1 / 2

Find the chord formula of the tangent point of the ellipse, the ellipse in the standard form X ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, through (P, q) as its two tangents, find the chord equation of the tangent point

Just remember, it's PX / A ^ 2 + QY / b ^ 2 = 1. It's very troublesome to prove strictly. Although the formula test is not so strict, it won't deduct points

What does the volume of a car's cylinder mean

The piston movement has top dead center and bottom dead center. The swept volume between top dead center and bottom dead center is the working volume of the cylinder. For a multi cylinder engine, the sum of the working volumes of all cylinders is the exhaust volume of the engine, that is, the displacement

The following questions are easy to calculate: 1, (5 / 8 + 5 / 8) times 4 / 25 2, (5 / 6-2 / 3) times 9 / 10
1. (5 / 8 + 5 / 8) times 4 / 25
2. (5 / 6-2 / 3) times 9 / 10
3. 1-7 / 9 divided by 7 / 8

1. (5 / 8 + 5 / 8) times 4 / 25 = 10 / 8 times 4 / 25 = 5 / 4 times 4 / 25 = 1 / 5
2. (5 / 6-2 / 3) times 9 / 10 = (5 / 6-4 / 6) times 4 / 6 = 1 / 9
3. 1-7 / 9 divided by 7 / 8 = 9 / 9-7 / 9 divided by 7 / 8 = 16 / 63

Differential equation √ (1 + y) DX + √ (1 + x) dy =?

This is a first order ordinary differential equation with separable variables
Separated variable [1 / √ (1 + x)] DX = [- 1 / √ (1 + y)] dy
Two side integral ∫ [1 / √ (1 + x)] DX = ∫ [- 1 / √ (1 + y)] dy
Rounding differential ∫ [1 / √ (1 + x)] d (1 + x) = ∫ [- 1 / √ (1 + y)] d (1 + y)
Integral and sort out √ (1 + x) + √ (1 + y) = C
Where C is an arbitrary constant

The water cement ratio of plain water slurry grouting is 1:0.5, and the water glass content is 5%. How much cement is used per cubic meter and how much water glass is used

Due to the different bulk density of different types of cement, the amount of cement in each cubic meter of cement slurry is different. Suppose that the bulk density of cement you use is 1400KG / m3. According to the water cement ratio of 1:0.5, the amount of cement in each cubic meter of cement slurry is 824kg, and the amount of sodium silicate is 41.2kg

Simplify logical expression a + A + A

Any logic and its own or logic are equal to the logic itself, so a + A + a = a
Any logic and its own and logic are equal to the logic itself, so a * a * a = a