The length of the major axis of the ellipse C: (x ^ 2) / (a ^ 2) + (y ^ 2) / (b ^ 2) = 1 (a > b > 0) is 4. If the point P is any point on the ellipse C, the line L passing through the origin is equal to the ellipse Intersect at two points m and N. note that the slopes of lines PM and PN are KPM and KPN respectively. When KPM * KPN = - 1 / 4, solve the elliptic equation

The length of the major axis of the ellipse C: (x ^ 2) / (a ^ 2) + (y ^ 2) / (b ^ 2) = 1 (a > b > 0) is 4. If the point P is any point on the ellipse C, the line L passing through the origin is equal to the ellipse Intersect at two points m and N. note that the slopes of lines PM and PN are KPM and KPN respectively. When KPM * KPN = - 1 / 4, solve the elliptic equation

The length of major axis is 4 a = 2 x ^ 2 / 4 + y ^ 2 / b ^ 2 = 1. Let l y = kxm (x1, kx1) n (- x1, - kx1) KPM = (y0-kx1) / (x0-x1) KPN = (Y0 + kx1) / (x0 + x1) KPM * KPN = - 1 / 4 (Y0 ^ 2-k ^ 2x1 ^ 2) / (x0 ^ 2-x1 ^ 2) = - 1 / 44y0 ^ 2-4k ^ 2x1 ^ 2 + x0 ^ 2-x1 ^ 2 = 0, Y0 ^ 2 = B ^ 2-B ^ 2

We know that the line L: y = - x + B and the ellipse C: x ^ 2 / 6 + y ^ 2 / 3 = 1 intersect at two different points a and B, (1) find the value range of B, (2) when the points a and B and the origin
It is known that the line L: y = - x + B and the ellipse C: x ^ 2 / 6 + y ^ 2 / 3 = 1 intersect at two different points a and B,
(1) Find the range of B;
(2) When points a, B and the origin form a right triangle with ab as the hypotenuse, the value of B is calculated
Quick, urgent, a

(1) X ^ 2 / 6 + y ^ 2 / 3 = 1 and y = - x + B are combined to get 3x ^ 2-4bx + 2B ^ 2-6 = 0
Delt>0,-3

The straight line L passing through the origin intersects with the curve C: x23 y2 = 1. If the length of the line segment cut by the curve C is not greater than the root 6, the straight line l will be straight
The line L passing through the origin intersects the curve C: x23 y2 = 1. If the length of the line L cut by the curve C is not greater than the root 6, then the value range of the inclination angle α of the line L is

The line passing through the origin L: y = KX, ① intersects the curve C: x ^ 2 / 3 + y ^ 2 = 1, ②,
Substituting ① into ②, x ^ 2 + 3K ^ 2x ^ 2 = 3,
(1+3k^2)x^2=3,
X = soil √ [3 / (1 + 3K ^ 2)],
The length of a line cut by curve C
=2√[3/(1+3k^2)]*√(k^2+1)

If point a (- 2, - 3), B (- 3, - 2), line L passes point P (1,1) and intersects line AB, then the slope k of L is ()
A. K ≤ 34 or K ≥ 43b. K ≤ - 43 or K ≥ - 34C. 34 ≤ K ≤ 43D. - 43 ≤ K ≤ - 34

∵ a (- 2, - 3), P (1,1) ∵ the slope of the line PA is kPa = 1 + 31 + 2 = 43. Similarly, the slope of the line Pb is KPB = 1 + 21 + 3 = 34 ∵ the line L passes through the point P (1,1) and intersects with the line AB, and the slope angle is always acute in the process of slope change. The value range of the slope k of the line Pb is 34 ≤ K ≤ 43, so C is selected