It is known that the eccentricity of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is root 6 / 3. A straight line Ma is made through a point m on the ellipse, and MB intersects the ellipse at two points a and B with slopes K1 and K2 respectively. If points a and B are symmetrical about the origin, the value of K1 · K2 is?

It is known that the eccentricity of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is root 6 / 3. A straight line Ma is made through a point m on the ellipse, and MB intersects the ellipse at two points a and B with slopes K1 and K2 respectively. If points a and B are symmetrical about the origin, the value of K1 · K2 is?

∵ points a and B are symmetric about the origin, ∵ let a (x1, Y1), B (- x1, - Y1), m (X2, Y2) ∵ K1 = (y1-y2) / (x1-x2), K2 = (Y1 + Y2) / (x1 + x2) ∵ K1 * K2 = ((y1-y2) / (x1-x2)) * ((Y1 + Y2) / (x2 + x1)) = (Y2 ^ 2-y1 ^ 2) / (x2 ^ 2-x1 ^ 2) and ∵ A and m on the ellipse, ∵ X1 ^ 2 / A ^ 2 + Y1 ^ 2 / b ^ 2 = 1

It is known that the center of the ellipse is at the origin, the focus is on the x-axis, the major axis is 12, the eccentricity is 1 / 3, and the ellipse is square
It is known that the center of the ellipse is at the origin, the focus is on the x-axis, the major axis is 12, and the eccentricity is 1 / 3

2a=12 a=6 c/a=1/3 c=2 b^2=a^2-c^2=32 x^2/36+y^2/32=1

It is known that the center of the ellipse C is at the origin of the coordinate system x0y, the eccentricity is half, and a focus is f (- 1,0). The equation of the ellipse C is solved

E = C / a = 1 / 2, the focus is on the Y axis, C = 1, a = 2, so the solution is x ^ 2 / 3 + y ^ 2 / 4 = 1

Let the center of the ellipse be at the origin, the focus be on the x-axis, and the eccentricity be half
Given that the farthest distance from the point P (0,2 / 3) to the point on the ellipse is the root sign 7, how to find the trajectory equation of the ellipse, the idea, no process, thank you

First, we use the eccentricity to get the relationship between a and B, so that there is only one parameter in the elliptic equation. Then we use the distance formula between two points to calculate the distance (square) between M and P on the ellipse. We use the elliptic equation to eliminate x ^ 2, and get a quadratic function with one parameter about y. after the formulation, we should pay attention to the value range of Y

It is known that the center of the ellipse C is at the origin of the coordinate system xoy, the eccentricity is 1 / 2, and a focus is f (- 1,0). (1) find the center of the ellipse C
In the exam, ask the netizens for help!

e=c/a=1/2
c=1,a=2,b2=3
x2/4+y2/3=1

If the focal length of an ellipse is equal to the length of its minor axis, then the eccentricity of the ellipse is equal to______ ．

According to the meaning of the question, C = B, and a = B2 + C2 = 2c, the eccentricity of the ellipse e = CA = 22, so the answer is 22

If the focal length of an ellipse is equal to the length of its half axis, what is the eccentricity of the ellipse?

If it is semimajor axis, then a = 2c, e = C / a = 1 / 2
If it is a semi minor axis, then B = 2c, a = √ [(2C) ^ 2 + C ^ 2] = √ 5C, e = C / a = √ 5 / 5

If the focal length of an ellipse is equal to the length of its minor axis, then the eccentricity of the ellipse is equal to ()
A. 12B. 22C. 2D. 2

Because the length of the short axis of the ellipse is equal to the focal length, that is, B = C, ∧ a = B2 + C2 = 2 & nbsp; C, ∧ CA = 22, B is chosen

We know that the center of the ellipse is at the origin, the focus is on the x-axis, and the eccentricity e = 1 / 3. We also know that the abscissa of a point m on the ellipse is equal to the abscissa of the right focus,
If the ordinate is 4, the equation of this ellipse can be solved

Let the elliptic equation (x ^ 2 / A ^ 2) + (y ^ 2 / b ^ 2) = 1 (a > b > 1)
∵ eccentricity e = 1 / 3 ∵ 3C = a, 9C ^ 2 = a ^ 2
∵a^2-b^2=c^2 ∴8c^2=b^2
The equation (x ^ 2 / 9C ^ 2) + (y ^ 2 / 8C ^ 2) = 1
∵ m its abscissa is equal to the abscissa of the right focus, and its ordinate is 4
Let m coordinate (C, 4)
∴(c^2/9c^)+(4^2/8c^2)=1
c^2=9/4
∴a^2=81/4,b^2=72/4
Equation: (4x ^ 2 / 81) + (4Y ^ 2 / 72) = 1

The abscissa of a point m on the ellipse is the same as that of the right focus, and the length of the ordinate is equal to 2 / 3 of the length of the short half axis

That is, (C, 2b / 3)
He is in X & sup2 / / A & sup2; + Y & sup2 / / B & sup2; = 1
c²/a²+(4b²/9)/b²=1
c²/a²+4/9=1
c²/a²=5/9
So e = C / a = √ 5 / 3