Taking the moving points P, F1 and F2 on the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1 as the focus, the trajectory equation of the center of gravity g of △ pf1f is obtained

Taking the moving points P, F1 and F2 on the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1 as the focus, the trajectory equation of the center of gravity g of △ pf1f is obtained

F1(-3,0),F2(3,0)
Let the center of gravity be g (x, y) (F1, F2, G are not collinear, y ≠ 0)
Using the coordinate formula of center of gravity
P(3x,3y)
P is on the ellipse,
So 9x ^ 2 / 25 + 9y ^ 2 / 16 = 1 (Y ≠ 0)

If the focal length, short axis length and long axis length of an ellipse form an equal ratio sequence, the eccentricity of the ellipse is 0______ ．

Let the focal length, short axis length and long axis length of the ellipse be 2c, 2b, 2A respectively, ∵ the focal length, short axis length and long axis length of the ellipse form an equal proportion sequence, ∵ 2c, 2b, 2A form an equal proportion sequence, ∵ 4B2 = 2A · 2c, ∵ B2 = a · C ∵ B2 = a2-c2 = a · C, divide both sides by A2 to get E2 + E-1 = 0, and E = 5 − 12, so the answer is: 5 − 12

If the focal length of an ellipse is known to be the equal ratio of the major axis length to the minor axis length, then the eccentricity of the ellipse is?

Because (2C) ^ 2 = 2A * 2B
So C ^ 2 = ab
So B = C ^ 2 / A
Because a ^ 2 = B ^ 2 + C ^ 2
So a ^ 2 = (C ^ 2 / a) ^ 2 + C ^ 2
So (C / a) ^ 4 + (C / a) ^ 2-1 = 0
So (C / a) ^ 2 = (- 1 ± √ (1 + 4)) / 2 = (√ 5-1) / 2 (negative value rounding off)
So e = C / a = √ [(√ 5-1) / 2]

If the major axis of the ellipse is long, the minor axis is long, and the focal length is in an equal ratio sequence, the eccentricity of the ellipse is calculated

Long axis 2A
Short axis 2B
Focal length 2C
(2b)^2=2a*2c
b^2=a^2-c^2
e=c/a
All that's left is to solve the equation, and you'll do it

The focal length of an ellipse is the equal proportion of the length of the major axis and the length of the minor axis

The focal length of an ellipse is the equal proportion of the length of the major axis and the length of the minor axis
Let the focal length | F1F2 | = 2C
Major axis length = 2A
Minor axis length = 2B
Proportional median
(2c)^2=4a*b
c^2=a*b
e=a/c=√(a^2/c^2)=√ab/a^2=√b/a
b^2=a^2-c^2
a^2-ab-b^2=0
Same division ab
a/b-b/a=1
Let B / a = X
x^2+x=1
(x+1/2)=5/4
x=√(5-1)/2
e=√(b/a)=√x=√[(5-1)/2]

P is the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ = 1. P is the ellipse m any point | Pf1 | PF2 maximum value | range is [2C ^ 2,3c ^ 2], then what is the value range of ellipse eccentricity e?

Let the coordinates of point P on the ellipse be p (x, y)
The ellipse defined by conic is: | Pf1 | = a + ex, | PF2 | = a-ex
So, | Pf1 | * | PF2 | = (a + Ex) (a-ex) = A & sup2; - E & sup2; X & sup2; a & sup2; that is: the maximum value of | Pf1 | Pf1 | is a & sup2;
Therefore, 2C & sup2; a & sup2; 3C & sup2;
So, 1 / 3C & sup2; 1 / A & sup2; 1 / 2C & sup2;
Therefore, 1 / 3 "C & sup2"; / A & sup2; "1 / 2"
So, (radical 3) / 3 "e" (radical 2) / 2 "
That is: the value range of ellipse eccentricity e is [(radical 3) / 3, (radical 2) / 2]

If the projection of the two intersection points of the straight line y = 22x and the ellipse x2a2 + y2b2 = 1, a > b > 0 on the X axis is exactly the two focal points of the ellipse, then the eccentricity e of the ellipse is equal to ()
A. 32B. 22C. 33D. 12

By substituting m into the elliptic equation, c2a2 + 12c2b2 = 1, B2 = a2-c2, which is reduced to 2c4-5a2c2 + 2a4 = 0, ∵ 2e4-5e2 + 2 = 0, ∵ 2e2-1) (E2-2) = 0, ∵ 0 < e < 1, ∵ 2e2-1 = 0, and the solution is e = 22

The square of 2x + the square of y = 8, find the focus and focal length of the ellipse

2x^2+y^2=8 ===>x^2/4+y^2/8=1
a^2=8 ,b^2=4 ,c=2
Focus (- 2,0) or (2,0) focal length = 4

How to determine the two focal points of ellipse with oblique section of cylinder

I don't know what you mean
Can two axes of symmetry of ellipse be drawn?
If you know the center, major axis and minor axis, just go through the endpoint of minor axis, draw a circle with major axis as radius, and the two intersections with major axis are focus

If the two focus positions of the ellipse are determined, is the ellipse uniquely determined?

Not sure
An ellipse is the locus of a point on a plane whose sum of the distances to two fixed points is a constant value. It can also be defined as the locus of a point whose ratio of the distance to a fixed point to the distance between a fixed line is a constant value less than 1. It is a kind of conic curve
The two fixed points F1 and F2 are called the focal points of the ellipse, and the distance between the two focal points │ F1F2 │ = 2C