The two focal points of the ellipse y2a2 + x2b2 = 1 (a > b > 0) are F1 (0, - C), F2 (0, c) (c > 0), the eccentricity e = 32, and the shortest distance from the focal point to the point on the ellipse is 2-3 | Math enthusiast | Mathematical art

The two focal points of the ellipse y2a2 + x2b2 = 1 (a > b > 0) are F1 (0, - C), F2 (0, c) (c > 0), the eccentricity e = 32, and the shortest distance from the focal point to the point on the ellipse is 2-3

∵ e = 32, the shortest distance from the focus to the point on the ellipse is 2-3, ∵ CA = 32, a-c = 2-3, the solution is a = 2, C = 3, ∵ B2 = a2-c2 = 1, thus the equation of the ellipse is y24 + x2 = 1

RELATED INFORMATIONS

1. If the focal length, minor axis length and major axis length of an ellipse form an arithmetic sequence, then the eccentricity is______ ．
2. If the length of the major axis, the length of the minor axis and the focal distance of an ellipse form an arithmetic sequence, then the eccentricity of the ellipse is zero______ ．
3. The eccentricity of an ellipse is () A. 45B. 35C. 25D. 15
4. If the length of the major axis, the length of the minor axis and the focal distance of an ellipse form an arithmetic sequence, then the eccentricity of the ellipse is zero______ ．
5. The eccentricity of an ellipse is () A. 45B. 35C. 25D. 15
6. If the major axis of an ellipse has the same length, the minor axis length and the focal distance form an arithmetic sequence, then the eccentricity is? How to calculate
7. If the focal length, minor axis length and major axis length of an ellipse form an arithmetic sequence, then the eccentricity is______ ．
8. 8. Given that the equation of ellipse C is, try to determine the value range of M, so that for a straight line, two different points on ellipse C are symmetrical about the straight line 8. It is known that the equation of ellipse C is x2 / 4 + Y2 / 3 = 1. Try to determine the value range of M, so that for the straight line y = 4x + m, there are two different points on ellipse C symmetrical about the straight line
9. It is known that the focal length of ellipse C equation is 4 and the equation of solving ellipse through P [√ 2, √ 3]
10. If the focal length of the ellipse x2m + y24 = 1 is 2, then the value of M is equal to______ ．
11. 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
12. 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
13. 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
14. A focal point is f (2 radical 3,0), a = 2c, find the analytic expression of ellipse
15. 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?
16. 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
17. 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.
18. 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
19. 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
20. 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