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Given the set a = {x | X & # 178; - 160}, find a ∪ B
The line y = x + 1 and ellipse 3x ^ 2 + y ^ 2 = 2 intersect at P and Q. The proof is that the circle with the diameter of the line PQ passes through the coordinate origin
By substituting y = x + 1 into 3x ^ 2 + y ^ 2 = 2, we get 3x ^ 2 + (x + 1) ^ 2 = 24x ^ 2 + 2x-1 = 0, XP * XQ = - 1 / 4; XP + XQ = - 2 / 4yp * YQ = (XP + 1) (XQ + 1) = XP * XQ + (XP + XQ) + 1 = - 1 / 4-2 / 4 + 1 = 1 / 4kpo * kqo = YP / XP * YQ / XQ = YP * YQ / (XP * XQ) = (1 / 4) / (- 1 / 4) = - 1, so Po is perpendicular to Qo, so o is in PQ
It is known that the right focus of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 is F2 (3,0) and the eccentricity is e. let the line y = KX intersect the ellipse at two points a and B, and m and N are line segments respectively
Af2, the midpoint of BF2. If the coordinate origin o is on the circle with Mn as the diameter, and √ 2 / 2 ＜ e ≤ √ 3 / 2, find the value range of K
Maybe my answer seems to be more troublesome: it's a fractional line, and the multiplication sign is omitted. Let a coordinate be (x1, kx1), and B coordinate be (X2, kx2) - which is reflected in the straight line y = KX. Using the midpoint coordinate formula, we can know m coordinate ((x1 + 3) / 2, kx1 / 2), n coordinate ((x2 + 3) / 2, kx2 / 2) because the origin o is on the circle with Mn as the diameter, so om ⊥ on
RELATED INFORMATIONS
- 1. Let L: y = KX + 2 and the square of ellipse C: 2 / x plus the square of Y 1 intersect at two different points a, B, O as the origin of coordinates, (1) find the straight range of K; (2) if OA. Ob = 1, find the equation of line L; (3) when k is the value, the area of triangle OAB will get the maximum value;
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- 7. Given that f (x) = x ^ 3-2x ^ 2 + X-2, if the extremum of function g (x) = f (x) + (1 / 3) MX exists, then the value range of real number m is?
- 8. When x ∈ [0,2], the function f (x) = ax ^ 2 + 4 (A-1) x-3 gets the maximum value when x = 2, then the value range of A
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- 10. If the image of function f (x) = (1-ax) / (1 + ax) (x is not equal to 1 / a) is symmetric with respect to y = x, then what is a?
- 11. The known set a = {XLX & # 178; - 4x + 3
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