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

Let there be two points a (x1, Y1), B (X2, Y2)
Then the midpoint m (x0, Y0) of AB is in the ellipse and on the straight line y = 4x + M
AB perpendicular to the line y = 4x + M
List known relationships:
3x1 ^ 2 + 4Y1 ^ 2 = 12... 1 (a on ellipse)
3x2 ^ 2 + 4y2 ^ 2 = 12... 2 (B on ellipse)
2x0 = X1 + X2.3 (M is the midpoint of AB)
2y0 = Y1 + y2.4 (ditto)
Y0 = 4x0 + m.5 (m on the line y = 4x + m)
(y1-y2) / (x1-x2) = - 1 / 4... 6 (AB perpendicular to the line y = 4x + m)
3x0^2+4y0^2

RELATED INFORMATIONS

1. It is known that the focal length of ellipse C equation is 4 and the equation of solving ellipse through P [√ 2, √ 3]
2. If the focal length of the ellipse x2m + y24 = 1 is 2, then the value of M is equal to______ ．
3. If the ellipse x ^ 2 / m ^ 2 + y ^ 2 / 4 = 1 passes through the point (- 2, √ 3), then its focal length is the required process. Thank you
4. If the focal length of the ellipse x2m + y24 = 1 is 2, then the value of M is equal to______ ．
5. If the focal length of ellipse x ^ 2 / M + y ^ 2 / 2 = 1 is the same as that of ellipse x ^ 2 / 8 + y ^ 2 / 18 = 1, then the value of M is?
6. If the focal length of ellipse x ^ 2 / m ^ 2 + y ^ 2 / 4 = 1 is 2, then the value of positive number m is 2______
7. Given that the elliptic equation is x28 + y2m2 = 1, the focal length is equal to () A. 28−m2B. 222−|m|C. 2m2−8D. 2|m|−22
8. Taking the vertex of the major axis of the ellipse with 25 / x square plus 9 / y square equal to 1 as the focus, the hyperbolic equation with the focus as the vertex is?
9. It is known that an ellipse with 4 / 2 of x plus 3 / 2 of Y equals 1, and a parabola with y equals 4x square Find the focal length of ellipse. 2, find the focal coordinate of parabola and the equation of collimator
10. Ellipse C rectangular coordinate equation 4 / x square + 3 / y square = 1, determine the value range of M, straight line L; y = 4x + m, there are two different points on ellipse C symmetrical about straight line L Please know the answer to this question friends, can give detailed and quick reply, thank you
11. If the focal length, minor axis length and major axis length of an ellipse form an arithmetic sequence, then the eccentricity is______ ．
12. 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
13. The eccentricity of an ellipse is () A. 45B. 35C. 25D. 15
14. 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______ ．
15. The eccentricity of an ellipse is () A. 45B. 35C. 25D. 15
16. 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______ ．
17. If the focal length, minor axis length and major axis length of an ellipse form an arithmetic sequence, then the eccentricity is______ ．
18. 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
19. 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
20. 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