It is known that the equation of ellipse C is 3xx + 4yy = 12, and the value range of M is obtained, so that two different points on the ellipse are symmetrical about the line This line: y = 4x + M I'm sorry I knocked it out

It is known that the equation of ellipse C is 3xx + 4yy = 12, and the value range of M is obtained, so that two different points on the ellipse are symmetrical about the line This line: y = 4x + M I'm sorry I knocked it out

2718 is wrong
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

The focal length of ellipse X / 4 + Y / 3 = 1 is equal to?

2C = 2 √ (a ^ 2-B ^ 2) = 2 √ (4-3) = 2 √ 1 = 2, that is, the focal length of the ellipse is 2

Given that the ellipse x ^ 2 / 10-m + y ^ 2 / m-2 = 1, the major axis is on the Y axis, if the focal length is 4, then M is equal to 1

y^2/(m-2)+x^2/(10-m)=1
The long axis is on the Y axis
m-2>10-m
m>6
The focal length is 4 = 2c, C = 2
m-2-10+m=c^2=4
m=8

Let the ellipse X / M + Y / 4 pass through the point (- 2, √ 3), then what is the focal length of the ellipse?

Substituting the point (- 2, √ 3) into the equation:
4/m²+3/4=1
4/m²=1/4
∴m²=4÷1/4=16
That is, a & # 178; = M & # 178; = 16
∵b²=4
∴c²=a²-b²=12
∴c=2√3
Focal length: 2C = 4 √ 3
If you are satisfied, please click [satisfied] in the upper right corner~

Let x ∧ 2 / m ∧ 2 + y ∧ 2 / 4 = 1 pass through the point (- 2, √ 3) to find the focal length of the ellipse?

Substituting the point (- 2, √ 3) into the equation:
4/m²+3/4=1
4/m²=1/4
∴m²=4÷1/4=16
That is, a & # 178; = M & # 178; = 16
∵b²=4
∴c²=a²-b²=12
∴c=2√3
Focal length: 2C = 4 √ 3

If the focal length of the ellipse x ^ 2 / 8 + y ^ 2 / m ^ 2 = 1 is 4, then the value of M is?
The answer is plus or minus 2 or plus or minus 2 root sign 3
But according to the ellipse formula is not a > b > 0, in the end can take negative

M can be positive or negative
The formula a > b > 0 has geometric meaning
A is the semi major axis length, B is the semi minor axis length, C is the semi focal length
When m is negative, it just has no geometric meaning. That's all. It's still an ellipse

If the focus of the ellipse on the x-axis is X & # 178; / M + Y & # 178; / 36 = 1 and the focal length is 2, then M=

2c=2
c=1
c^2=1
b^2=36
a^2=m
m-36=1
m=36+1
m=37

If the focal length of the ellipse M / x square + 2 / y square = 1 is the same as that of the ellipse M / x square + 18 / y square = 1, then the value of M is

The focal length of 8 / x square + 18 / y square = 1 is
C square = 18-8 = 10
M / x square + 2 / y square = 1
Csquare = m-2 = 10
M=12

Let m be a positive real number. If the focal length of the ellipse x2m2 + 16 + Y29 = 1 is 8, then M=______ ．

∵ A2 = M2 + 16, B2 = 9, ∵ C2 = M2 + 16-9 = M2 + 7, ∵ 2C = 8, ∵ M & nbsp; 2 + 7 = 4, {M = 3, so the answer is: 3

What is the equation of ellipse (x square) / 4 + (y Square) with respect to a symmetric ellipse of line y = x-3?

Let any point P (x1, Y1) on the ellipse x ^ 2 / 4 + y ^ 2 = 1 be symmetric with respect to the straight line y = x-3, then q (x, y) has: {(Y1 + y) / 2 = (x1 + x) / 2-3, ((y1-y) / (x1-x)) * 1 = - 1} solution: X1 = y + 3, Y1 = x-3 ∵ point P (x1, Y1) on the ellipse ∵ substitute ellipse: x ^ 2 / 4 + y ^ 2 = 1