The focal length of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 is 2C. If the three numbers a, B and C form an equal ratio sequence in turn, calculate the eccentricity E

∵ B ^ = AC = a ^ 2-C ^ 2, divide both sides by a ^ 2 to get e ^ 2 + E-1 = 0, ∵ 0

RELATED INFORMATIONS

1. If the point P (C, 2C) is in the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0), then the eccentricity of the ellipse E= Such as the title
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
3. If the half focal length of the ellipse x ^ 2 / A ^ 2 + y ^ / b ^ 3 = 1, (a > b > 0) is C, and the abscissa of the straight line y = 2x and a focus of the ellipse is exactly C, then the eccentricity of the ellipse
4. How to determine the focus of the ellipse Some answer questions, Taking the long and short axis of the ellipse as the center and the short axis as the diameter, draw a circle, and the intersection of the long axis of symmetry is the focus of the ellipse.
5. P is the point F1 on the x-axis ellipse x2a2 + y2b2 = 1, F2 is the two focal points of the ellipse, and the half focal length of the ellipse is C, then the difference between the maximum and minimum value of | Pf1 | · | PF2 | must be () A. 1B. a2C. b2D. c2
6. If P is a point on a fixed ellipse (the length of major axis, the length of minor axis and the length of focal length are 2a, 2b and 2C respectively, and the focus is F1 and F2), If the maximum value of | Pf1 | PF2 | is 16 and the minimum value is 7, then what are a and B equal to? Why?
7. A focal point is f (2 radical 3,0), a = 2c, find the analytic expression of ellipse
8. It is known that the left and right focal points of ellipse C: x2a2 + y2b2 = 1 (A & gt; B & gt; 0) are F1 and F2 respectively, the eccentricity e = 12, and the line y = x + 2 passes through the left focal point F1. (1) find the equation of ellipse C; (2) if P is a point on ellipse C, find the range of ∠ f1pf2
9. It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) e = √ 2 / 2, the left and right focal points are F1, F2 and P (2, √ 3) Let the line L: y = KX + m intersect with the ellipse C at two points M. n. the inclination angles of the lines F2m and f2n are α, β, and α + β = π (PIE). Let's ask whether the line L passes the fixed point? If so, find the coordinates of the point
10. It is known that the left and right focal points of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 are F1 and F2 half focal length is c. the chord f1m of the ellipse is made through F1 and extended to N, so that Mn = MF2. It is proved that the trajectory of n is a circle and its equation is solved
11. It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a is greater than B is greater than 0) is root sign 2 / 2, and its left and right focuses are F1F2 respectively. P is a point on the ellipse. Vector Pf1 × vector PF2 = 3 / 4, absolute value of OP = root sign 7 / 2 1. Solving the equation of ellipse C 2. The moving line L passing through point s (0, - 1 / 3) intersects with ellipse C and a, B. question: is there a fixed point m on the y-axis so that a circle with diameter AB passes through point m? If there is, find out the coordinates of M. if not, explain the reason
12. Let AB be the chord passing through the center of the ellipse and f be a focal point of the ellipse? The ellipse is x ^ 2 + 2Y ^ 2 = 1
13. If the hyperbola X29 − y2 = 1 has moving points P, F1 and F2, then the trajectory equation of the center of gravity m of △ pf1f2 is______ ．
14. There is a moving point P on the ellipse X / 9 + y2 = 1. F1 and F2 are the two focal points of the ellipse. The trajectory equation of the center of gravity m of △ pf1f2 is obtained
15. It is known that F 1 and F 2 are the left and right focal points of the ellipse C: x 24 + y 23 = 1 respectively, and P is the moving point on the ellipse C, then the trajectory equation of the center of gravity g of △ pf1f 2 is () A. x236+y227＝1(y≠0)B. 4x29+y2＝1(y≠0)C. 9x24+3y2＝1(y≠0)D. x2+4y23＝1(y≠0)
16. If the hyperbola X29 − y2 = 1 has moving points P, F1 and F2, then the trajectory equation of the center of gravity m of △ pf1f2 is______ ．
17. If F1 and F2 are the focus of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1, and P is the point on the ellipse that is not on the X axis, then the trajectory equation of the center of gravity g of △ pf1f2 is
18. Ellipse x ^ 2 / A ^ 2 + y ^ 2 = 1, triangle ABC takes a (0,1) as the right vertex, B, C on the ellipse, the maximum area of triangle is 27 / 8, find the value of A
19. Let the center of the ellipse C be at the origin, the focus on the Y axis, and the eccentricity be 2 / 2 of the root sign 1. Find the standard equation of ellipse C 2. If the line L with slope 2 passes through the focus of ellipse C on the positive half axis of Y axis and intersects with the ellipse at two points AB, then | AB is obtained|
20. It is known that the left and right focal points of the ellipse x ^ 2 / 2 + y ^ 2 / 1 = 1 are F1 and F2 respectively. If the straight line passing through point P (0, - 2) and F1 intersects the ellipse at two points a and B, find the triangle ABF It is known that the left and right focal points of the ellipse x ^ 2 / 2 + y ^ 2 / 1 = 1 are F1 and F2 respectively. If the straight line passing through point P (0, - 2) and F1 intersects the ellipse at two points a and B, the area of triangle abf2 is calculated