If the equation x ^ 2 / M + 4-y ^ 2 / M-6 = 1 represents an ellipse, then the value range of M is

If the equation x ^ 2 / M + 4-y ^ 2 / M-6 = 1 represents an ellipse, then the value range of M is

For an ellipse, then x ^ 2 / (M + 4) + y ^ 2 / (- M + 6) = 1
So m + 4 > 0, - M + 6 > 0
-4

Given the equation x ^ 2 / 4 + y ^ 2 / 3 = 1 of ellipse C, try to determine the value range of M
So that for the line y = ax + m, there are two different points on the ellipse C symmetrical about the line
Y = ax + m should be changed to y = 4x + M

Use the point difference method!
Let a (x1, Y1) B (X2, Y2), AB midpoint m (x0, Y0)
(x1)^2/4+(y1)^2/3=1...1
(x2)^2/4+(y2)^2/3=1...2
1-2 is (1 / 4) (x1 + x2) (x1-x2) + (1 / 3) (Y1 + Y2) (y1-y2) = 0
KAB = (x1-x2) / (y1-y2) = (1 / 4x0) / (- 1 / 3y0) = - 1 / 4 (middle vertical)
Launch Y0 = 3x0 launch m (x0,3x0)
M is on L again
Substituting into L equation m (- m, - 3M)
Finally, M is substituted into the elliptic equation to make it less than 1
The range of M
I bet it's right, our teacher said it!

It is known that the focus of the ellipse x ^ 2 / 9 + y ^ 2 / m ^ 2 = 1 is on the X axis, and the value range of M

9> M & # 178;, and M & # 178; ≠ 0
The solution is: - 3

If the equation x & # 178 / / 2-m + Y & # 178 / / 1 + M = 1 represents an ellipse, find the value range of M

Ellipse
Then 2-m > 0, M0, M > - 1
And the denominator cannot be equal, otherwise it is a circle
2-m≠1+m
So - 1

If the directrix of the ellipse X & # 178 / / M + Y & # 178; = 1 is parallel to the Y axis, then the value range of M is

In this problem, just note that the Quasilinear equation is x = A & # / C

It is known that the line L: y = x + m intersects the ellipse x220 + Y25 = 1 at two different points a, B, and the point m (4,1) is the fixed point. (1) find the value range of M; (2) if the line L is no more than the point m, prove that the line Ma, MB and the X axis form an isosceles triangle

(1) Substituting line L: y = x + m into ellipse x220 + Y25 = 1, we can get 5x2 + 8mx + 4m2-20 = 0 ∵ line L: y = x + m intersects ellipse x220 + Y25 = 1 at two different points a, B, ∵ Δ= 64m2-20 (4m2-20) > 0, ∵ 5 < m < 5; (2) prove that let the slopes of line Ma and MB be K1, K2, a (x1

Given that the equation x & # 178 / / M-1 + Y & # 178 / / 2-m = 1 represents an ellipse, find the value range of M

M-1 > 0, 2-m > 0, 1

If the line y-kx-1 = 0 (K ∈ R) and the ellipse X25 + y2m = 1 have a common point, then the value range of M is & nbsp; ()
A. M ＞ 5B. 0 ＜ m ＜ 5C. M ＞ 1D. M ≥ 1 and m ≠ 5

The straight line y = KX + 1 passes through the point (0, 1), and the straight line y = KX + 1 and the ellipse have a common point. Therefore, when (0, 1) on the ellipse or in the ellipse ﹥ 0 + 1m ≤ 1 ﹥ m ≥ 1 and M = 25, the curve is a circle or not an ellipse, so m ≠ 25 the value range of real number m is: m ≥ 1 and m ≠ 25, so select D

If the equation x squared / k-7 minus y squared / K-13 = 1 represents an ellipse with focus on the X axis, then the range of the real number k is?

x²/(k-7)+y²/(13-k)=1
ellipse
k-7>0,13-k>0
seven hundred and ten
So 10

If the equation x squared / k-7-y squared / K-13 = 1 denotes an ellipse with focus on the X axis, then the range of the real number k

k-7>0
k-13